The inhomogeneous p-Laplacian equation with Neumann boundary conditions in the limit p

We investigate the limiting behavior of solutions to the inhomogeneous p -Laplacian equation − Δ p u = μ p subject to Neumann boundary conditions. For right-hand sides, which are arbitrary signed measures, we show that solutions converge to a Kantorovich potential associated with the geodesic Wasser...

Full description

Saved in:
Bibliographic Details
Published inAdvances in continuous and discrete models Vol. 2023; no. 1; p. 8
Main Author Bungert, Leon
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2023
Springer Nature B.V
Subjects
Analysis
Approximation
Boundary conditions
Difference and Functional Equations
Functional Analysis
Investigations
Laplace equation
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Viscosity
Viscosity solution
35D30
Wasserstein distance
35D40
Infinity Laplacian
49Q22
Optimal transport
Laplacian
Online AccessGet full text

Cover

Abstract We investigate the limiting behavior of solutions to the inhomogeneous p -Laplacian equation − Δ p u = μ p subject to Neumann boundary conditions. For right-hand sides, which are arbitrary signed measures, we show that solutions converge to a Kantorovich potential associated with the geodesic Wasserstein-1 distance. In the regular case with continuous right-hand sides, we characterize the limit as viscosity solution to an infinity Laplacian / eikonal type equation.
AbstractList We investigate the limiting behavior of solutions to the inhomogeneous p-Laplacian equation −Δpu=μp subject to Neumann boundary conditions. For right-hand sides, which are arbitrary signed measures, we show that solutions converge to a Kantorovich potential associated with the geodesic Wasserstein-1 distance. In the regular case with continuous right-hand sides, we characterize the limit as viscosity solution to an infinity Laplacian / eikonal type equation.
We investigate the limiting behavior of solutions to the inhomogeneous p -Laplacian equation − Δ p u = μ p subject to Neumann boundary conditions. For right-hand sides, which are arbitrary signed measures, we show that solutions converge to a Kantorovich potential associated with the geodesic Wasserstein-1 distance. In the regular case with continuous right-hand sides, we characterize the limit as viscosity solution to an infinity Laplacian / eikonal type equation.
Author Bungert, Leon
Author_xml – sequence: 1
  givenname: Leon
  orcidid: 0000-0002-6554-9892
  surname: Bungert
  fullname: Bungert, Leon
  email: leon.bungert@hcm.uni-bonn.de
  organization: Hausdorff Center for Mathematics, University of Bonn
BookMark eNpFkEtLAzEURoMoWGv_gKuA6-hNMnktpfiCopvqNqSZTJvSJtPJDOK_d2oFV3dxD-eDc4XOU04BoRsKd5RqeV8ol5IRYJwAV6Ii-gxNmOKUVIyLczShUitCNTeXaFbKFgCYYVyBnqDP5SbgmDZ5n9chhTwU3JKFa3fOR5dwOAyujznhr9hv8FsY9i4lvMpDql33jX1OdTz-y-jA_ajaxX3scXuNLhq3K2H2d6fo4-lxOX8hi_fn1_nDgrS0YpoEv5JmBSCb4MFLBVQG3TglhDMyuMqAUYp65R2vNAdeuUZDDbqupDCiFnyKbk_etsuHIZTebvPQpXHSMjXqtAFtRoqfqNJ2Ma1D909RsMeG9tTQjg3tb0Or-Q9GfmXc
Cites_doi 10.1007/978-0-387-70914-7
10.1090/S0273-0979-1992-00266-5
10.1137/140975528
10.1090/cams/11
10.1515/anona-2022-0258
10.1515/anona-2017-0005
10.1017/S0308210506000667
10.1023/A:1024751022715
10.1007/s002050050157
10.1007/s11854-017-0019-2
10.1007/s00526-020-01883-6
10.1016/j.na.2005.11.030
ContentType Journal Article
Copyright The Author(s) 2023
The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: The Author(s) 2023
– notice: The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID C6C
3V.
7SC
7TB
7XB
8AL
8FD
8FE
8FG
8FK
ABJCF
ABUWG
AFKRA
ARAPS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
FR3
GNUQQ
HCIFZ
JQ2
K7-
KR7
L6V
L7M
L~C
L~D
M0N
M7S
P5Z
P62
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
Q9U
DOI 10.1186/s13662-023-03754-8
DatabaseName Springer Nature OA Free Journals
ProQuest Central (Corporate)
Computer and Information Systems Abstracts
Mechanical & Transportation Engineering Abstracts
ProQuest Central (purchase pre-March 2016)
Computing Database (Alumni Edition)
Technology Research Database
ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Central (Alumni) (purchase pre-March 2016)
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Central
Technology Collection
ProQuest One Community College
ProQuest Central Korea
Engineering Research Database
ProQuest Central Student
SciTech Premium Collection
ProQuest Computer Science Collection
Computer Science Database
Civil Engineering Abstracts
ProQuest Engineering Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
Computing Database
Engineering Database
Advanced Technologies & Aerospace Database
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Premium
ProQuest One Academic
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
ProQuest Central Basic
DatabaseTitle Publicly Available Content Database
Computer Science Database
ProQuest Central Student
Technology Collection
Technology Research Database
Computer and Information Systems Abstracts – Academic
ProQuest One Academic Middle East (New)
Mechanical & Transportation Engineering Abstracts
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
ProQuest Central Korea
ProQuest Central (New)
Advanced Technologies Database with Aerospace
Engineering Collection
Advanced Technologies & Aerospace Collection
Civil Engineering Abstracts
ProQuest Computing
Engineering Database
ProQuest Central Basic
ProQuest Computing (Alumni Edition)
ProQuest One Academic Eastern Edition
ProQuest Technology Collection
ProQuest SciTech Collection
Computer and Information Systems Abstracts Professional
Advanced Technologies & Aerospace Database
ProQuest One Academic UKI Edition
Materials Science & Engineering Collection
Engineering Research Database
ProQuest One Academic
ProQuest One Academic (New)
ProQuest Central (Alumni)
DatabaseTitleList Publicly Available Content Database
Database_xml – sequence: 1
  dbid: C6C
  name: Springer Nature OA Free Journals
  url: http://www.springeropen.com/
  sourceTypes: Publisher
– sequence: 2
  dbid: 8FG
  name: ProQuest Technology Collection
  url: https://search.proquest.com/technologycollection1
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
Engineering
EISSN 2731-4235
1687-1847
ExternalDocumentID 10_1186_s13662_023_03754_8
GrantInformation_xml – fundername: Vetenskapsrådet
  grantid: 2016-06596
  funderid: http://dx.doi.org/10.13039/501100004359
– fundername: Rheinische Friedrich-Wilhelms-Universität Bonn (1040)
– fundername: Deutsche Forschungsgemeinschaft
  grantid: 390685813
  funderid: http://dx.doi.org/10.13039/501100001659
GroupedDBID 0R~
AAJSJ
AAKKN
ABDBF
ABEEZ
ACACY
ACULB
AFGXO
ALMA_UNASSIGNED_HOLDINGS
C24
C6C
EBLON
EBS
ESX
RSV
SOJ
TUS
~8M
23M
2WC
3V.
4.4
40G
5GY
5VS
6J9
7SC
7TB
7XB
8AL
8FD
8FE
8FG
8FK
8R4
8R5
AAFWJ
ABJCF
ABUWG
ACGFO
ACGFS
ACIPV
ACIWK
ADBBV
AEGXH
AENEX
AFKRA
AFPKN
AHBYD
AHYZX
AIAGR
AMKLP
AMTXH
ARAPS
AZQEC
BAPOH
BCNDV
BENPR
BGLVJ
BPHCQ
CCPQU
CS3
DWQXO
FR3
GNUQQ
GROUPED_DOAJ
HCIFZ
J9A
JQ2
K6V
K7-
KQ8
KR7
L6V
L7M
L~C
L~D
M0N
M7S
OK1
OVT
P2P
P62
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PROAC
PTHSS
Q2X
Q9U
REM
RHU
RNS
SMT
U2A
UPT
ID FETCH-LOGICAL-p1428-ecb69b006fec0c67016e8fa755a96ea4909771c7ca3483034af80d08d46595d53
IEDL.DBID BENPR
ISSN 1687-1839
IngestDate Fri Jul 25 11:03:30 EDT 2025
Fri Feb 21 02:44:44 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Keywords Viscosity solution
35D30
Wasserstein distance
35D40
Infinity Laplacian
49Q22
Optimal transport
Laplacian
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-p1428-ecb69b006fec0c67016e8fa755a96ea4909771c7ca3483034af80d08d46595d53
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0002-6554-9892
OpenAccessLink https://www.proquest.com/docview/2770189089?pq-origsite=%requestingapplication%
PQID 2770189089
PQPubID 237355
ParticipantIDs proquest_journals_2770189089
springer_journals_10_1186_s13662_023_03754_8
PublicationCentury 2000
PublicationDate 2023-12-01
PublicationDateYYYYMMDD 2023-12-01
PublicationDate_xml – month: 12
  year: 2023
  text: 2023-12-01
  day: 01
PublicationDecade 2020
PublicationPlace Cham
PublicationPlace_xml – name: Cham
– name: New York
PublicationSubtitle Theory and Modern Applications
PublicationTitle Advances in continuous and discrete models
PublicationTitleAbbrev Adv Cont Discr Mod
PublicationYear 2023
Publisher Springer International Publishing
Springer Nature B.V
Publisher_xml – name: Springer International Publishing
– name: Springer Nature B.V
References Brezis (CR16) 2011
Lellmann, Lorenz, Schönlieb, Valkonen (CR18) 2014; 7
Buccheri, Leonori (CR22) 2021; 60
Mazón, Rossi, Toledo (CR4) 2014; 3
Lindqvist (CR13) 2017
Ziemer (CR17) 2012
Amato, Lia Masiello, Nitsch, Trombetti (CR19) 2022; 11
Crandall, Ishii, Lions (CR20) 1992; 27
CR11
Medina, Ochoa (CR21) 2019; 8
Peral, García Azorero, Manfredi, Rossi (CR6) 2009; 20
Bhattacharya, DiBenedetto, Manfredi (CR1) 1989; 47
García Azorero, Manfredi, Peral, Rossi (CR2) 2007; 66
Bouchitte, Buttazzo, De Pascale (CR3) 2003; 118
Juutinen, Lindqvist, Manfredi (CR7) 1999; 148
Calder, Cook, Thorpe, Slepčev (CR12) 2020
Evans, Gangbo (CR5) 1999
Esposito, Kawohl, Nitsch, Trombetti (CR8) 2015; 26
Bungert, Korolev (CR9) 2022; 2
Rossi, Saintier (CR15) 2016; 42
Lindgren, Lindqvist (CR14) 2017; 132
Champion, De Pascale (CR10) 2007; 137
References_xml – year: 2011
  ident: CR16
  publication-title: Functional Analysis, Sobolev Spaces and Partial Differential Equations
  doi: 10.1007/978-0-387-70914-7
– volume: 27
  start-page: 1
  issue: 1
  year: 1992
  end-page: 67
  ident: CR20
  article-title: User’s guide to viscosity solutions of second order partial differential equations
  publication-title: Bull. Am. Math. Soc.
  doi: 10.1090/S0273-0979-1992-00266-5
– volume: 42
  start-page: 613
  issue: 2
  year: 2016
  end-page: 635
  ident: CR15
  article-title: On the first nontrivial eigenvalue of the ∞-Laplacian with Neumann boundary conditions
  publication-title: Houst. J. Math.
– year: 1999
  ident: CR5
  publication-title: Differential Equations Methods for the Monge–Kantorovich Mass Transfer Problem
– volume: 7
  start-page: 2833
  issue: 4
  year: 2014
  end-page: 2859
  ident: CR18
  article-title: Imaging with Kantorovich–Rubinstein discrepancy
  publication-title: SIAM J. Imaging Sci.
  doi: 10.1137/140975528
– volume: 2
  start-page: 345
  issue: 8
  year: 2022
  end-page: 373
  ident: CR9
  article-title: Eigenvalue problems in : optimality conditions, duality, and relations with optimal transport
  publication-title: Commun. Am. Math. Soc.
  doi: 10.1090/cams/11
– volume: 11
  start-page: 1631
  issue: 1
  year: 2022
  end-page: 1649
  ident: CR19
  article-title: On the solutions to -Poisson equation with Robin boundary conditions when p goes to +∞
  publication-title: Adv. Nonlinear Anal.
  doi: 10.1515/anona-2022-0258
– volume: 8
  start-page: 468
  issue: 1
  year: 2019
  end-page: 481
  ident: CR21
  article-title: On viscosity and weak solutions for non-homogeneous -Laplace equations
  publication-title: Adv. Nonlinear Anal.
  doi: 10.1515/anona-2017-0005
– volume: 137
  start-page: 1179
  issue: 6
  year: 2007
  end-page: 1195
  ident: CR10
  article-title: Asymptotic behaviour of nonlinear eigenvalue problems involving -Laplacian-type operators
  publication-title: Proc. R. Soc. Edinb., Sect. A, Math.
  doi: 10.1017/S0308210506000667
– volume: 20
  start-page: 111
  issue: 2
  year: 2009
  end-page: 126
  ident: CR6
  article-title: The limit as for the -Laplacian with mixed boundary conditions and the mass transport problem through a given window
  publication-title: Rend. Lincei
– ident: CR11
– volume: 118
  start-page: 1
  issue: 1
  year: 2003
  end-page: 25
  ident: CR3
  article-title: A -Laplacian approximation for some mass optimization problems
  publication-title: J. Optim. Theory Appl.
  doi: 10.1023/A:1024751022715
– year: 2017
  ident: CR13
  publication-title: Notes on the -Laplace Equation
– volume: 148
  start-page: 89
  issue: 2
  year: 1999
  end-page: 105
  ident: CR7
  article-title: The ∞-eigenvalue problem
  publication-title: Arch. Ration. Mech. Anal.
  doi: 10.1007/s002050050157
– volume: 3
  start-page: 133
  issue: 3
  year: 2014
  end-page: 140
  ident: CR4
  article-title: Mass transport problems obtained as limits of -Laplacian type problems with spatial dependence
  publication-title: Adv. Nonlinear Anal.
– volume: 132
  start-page: 217
  issue: 1
  year: 2017
  end-page: 228
  ident: CR14
  article-title: Regularity of the -Poisson equation in the plane
  publication-title: J. Anal. Math.
  doi: 10.1007/s11854-017-0019-2
– volume: 60
  start-page: 1
  issue: 1
  year: 2021
  end-page: 23
  ident: CR22
  article-title: Large solutions to quasilinear problems involving the -Laplacian as diverges
  publication-title: Calc. Var. Partial Differ. Equ.
  doi: 10.1007/s00526-020-01883-6
– volume: 47
  start-page: 15
  year: 1989
  end-page: 68
  ident: CR1
  article-title: Limits as of and related extremal problems
  publication-title: Rend. Sem. Mat. Univ. Politec. Torino
– volume: 26
  start-page: 119
  issue: 2
  year: 2015
  end-page: 134
  ident: CR8
  article-title: The Neumann eigenvalue problem for the ∞-Laplacian
  publication-title: Rend. Lincei Mat. Appl.
– volume: 66
  start-page: 349
  issue: 2
  year: 2007
  end-page: 366
  ident: CR2
  article-title: The Neumann problem for the ∞-Laplacian and the Monge–Kantorovich mass transfer problem
  publication-title: Nonlinear Anal., Theory Methods Appl.
  doi: 10.1016/j.na.2005.11.030
– start-page: 1306
  year: 2020
  end-page: 1316
  ident: CR12
  article-title: Poisson learning: graph based semi-supervised learning at very low label rates
  publication-title: International Conference on Machine Learning
– year: 2012
  ident: CR17
  publication-title: Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation
SSID ssj0002923708
ssj0029488
Score 2.3167028
Snippet We investigate the limiting behavior of solutions to the inhomogeneous p -Laplacian equation − Δ p u = μ p subject to Neumann boundary conditions. For...
We investigate the limiting behavior of solutions to the inhomogeneous p-Laplacian equation −Δpu=μp subject to Neumann boundary conditions. For right-hand...
SourceID proquest
springer
SourceType Aggregation Database
Publisher
StartPage 8
SubjectTerms Analysis
Approximation
Boundary conditions
Difference and Functional Equations
Functional Analysis
Investigations
Laplace equation
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Viscosity
SummonAdditionalLinks – databaseName: Springer Nature OA Free Journals
  dbid: C6C
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV25TgMxELUgNFAgThEIyAUlFrbXa3tLFBFFCFIRlG7lKwIJNicFf8_YuwmHaKjX62KepXlzvUHoElw2tdJxYpWiRHCakcJ6Q0yhguNASbVJ3RYD2R-Ku1E-amRy4izM9_o90_J6wTIpOQHPQtK2VqI30VbOMhXXNHRld51P4cBUFNWruZg_f_3BIn8VPpM_6e2h3YYI4psauX20EaoDtPOwVlFdHKInwBC_VM-TtwnAHCBGx1Nyb2IbFYCKw6yW6cYxl4oHIabjK2zTnqT5B4ZA19f9WHAHhmvxaxxmwtMjNOzdPnb7pNmDQKZRD40EZ2WULpTj4KiTClha0GOj8twUMhhRUCBxzClnMqHBJQkz1tRT7UUUC_R5doxa1aQKJwgbb13UmGeKOsENs1p5nQVPrTOSGtVGnZWFyuYxL0oOMDIdC4RtdLWy2tfnFEZoWdb2LsHeZbJ3qU__d_wMbcdl7nWzSAe1lvP3cA4uf2kvEtafsF2kYw
  priority: 102
  providerName: Springer Nature
Title The inhomogeneous p-Laplacian equation with Neumann boundary conditions in the limit p
URI https://link.springer.com/article/10.1186/s13662-023-03754-8
https://www.proquest.com/docview/2770189089
Volume 2023
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV07T8MwED5Bu8CAeIpCqTwwYtVJXMeZUKlaqgpVCCjqFvlVgQTpk4F_zzlJKTCwZEikG-6cu-8evg_gEkM208KEVMcxozxkEU20VVQlsTMhQlKp8mmLoeiP-GDcGpcFt2U5Vrn2ibmjtlPja-TNEGUF0neprmdz6lmjfHe1pNDYhiq6YCkrUL3pDu8fvlOuhOfMk4HAX8ljgfW1GSmayyASIqQYs2jOA0vlL5D5py-ah5vePuyVOJG0C8MewJbLDmH3x_bAI3hGE5PX7GX6PsVT4DCFJzN6p_yUFdqcuHmxxZv4UisZOl-tz4jOaZQWnwTzYFuMa6EMgjCQvPm7TmR2DKNe96nTpyVNAp35dWnUGS38ZkMxcYYZgWoSTk5U3GqpRDjFE4YYLzCxURGXGLG4mkhmmbTc7xK0regEKtk0c6dAlNXGr6APYmZ4qAItYysjZ5k2SjAV16C-1lBanvVlurFMDa7WWtt8zrMMKdJC3ynqO831ncqz_6Wdw47ndi9mR-pQWS0-3AUigJVuwLbs3Tag2m4PHgeN0uj4thNy_xSdL3BBsmI
linkProvider ProQuest
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LLwRBEO4IBxzEMx6LPnDT0TPT29NzEBGsxdoT4jb6tSFhZlkb8af8RlU9O14HN-dO6lBdXfVV1-MjZAtCNjfSxsykKWci5gnLjNNMZ6m3MUBSpUO3RVe2r8TZTfNmjLzXszDYVln7xOCoXWnxj3w3BlmRwirVfv-JIWsUVldrCo3KLM792yukbIO90yO43-04bh1fHrbZiFWA9XG7GPPWSFwEKHvecitBqvSqp9NmU2fSa5FxgESRTa1OhAIHL3RPcceVE7h6zyFLBLj8CZFAJMfJ9NbJZ4KXicBzGUl4uIg86iEdJXcHUSJlzCBCssA6y9QPSPurChuCW2uWzIxQKT2ozGiOjPlinkx_21W4QK7BoOh9cVc-lmBzvhwOaJ91NPZ0gYVR_1TtDKf4sUu7HmsDBTWBtOn5jULW7armMJBBAXTSB5ysov1FcvUv6lsi40VZ-GVCtTMWF95HKbci1pFRqVOJd9xYLblOV0ij1lA-elmD_MsOVshOrbWv45DTKJlX-s5B33nQd65W_5a2SSbblxedvHPaPV8jU8gqX3WtNMj4y_PQrwP2eDEb4cIpuf1vC_sASgTogQ
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LTxsxEB5FQaraQ9WWokKh-AA3rHgfsb2HqqKFKJAoQqipclv8ikCC3UBAFX-tv64z--DRQ2-cV_JK488z33jG8wHsYMgWVrqYW6UET2OR8Mx6w02mgouRkmpTdVtM5HCaHs_6sw78ad_CUFtl6xMrR-1LR3fkvRjXijRVqXrzpi3i5GDwbXHNSUGKKq2tnEYNkVG4_43p2_Lr0QHu9W4cDw5__hjyRmGAL2jSGA_OShoKKOfBCSfxDzLouVH9vslkMGkmkB5FTjmTpBqdfWrmWnihfUpj-DwpRqD7X1GUFXVh5fvh5OT0Id3L0kr1MpJ4jImHtE92tOwto0TKmGO85JUGLdfPCO4_Ndkq1A3ewduGo7L9GlTvoROKD_DmyeTCVfiF8GIXxXl5VSICQ3m3ZAs-NtThhXhj4bqeIM7ompdNAlUKCmYrCaebe4Y5uK9bxXANhhSUXdI7K7b4CNMXMeAadIuyCJ-AGW8djb-PlHBpbCKrlddJ8MI6I4VR67DZWihvztkyf0TFOuy1Vnv8XGU4Wua1vXO0d17ZO9cb_19tG14huvLx0WT0GV6TxHzdwrIJ3dubu7CFROTWfml2nMHZS4PsL_YE7hM
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=The+inhomogeneous+p-Laplacian+equation+with+Neumann+boundary+conditions+in+the+limit+p&rft.jtitle=Advances+in+difference+equations&rft.au=Bungert%2C+Leon&rft.date=2023-12-01&rft.pub=Springer+Nature+B.V&rft.issn=1687-1839&rft.eissn=1687-1847&rft.volume=2023&rft.issue=1&rft.spage=8&rft_id=info:doi/10.1186%2Fs13662-023-03754-8&rft.externalDBID=HAS_PDF_LINK
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1687-1839&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1687-1839&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1687-1839&client=summon