A stationary heat conduction problem in low dimensional sets in RN

We study a basic linear elliptic equation on a lower dimensional rectifiable set S in R N with the Neumann boundary data. Set S is a support of a finite Borel measure μ . We will use the measure theoretic tools to interpret the equation and the Neumann boundary condition. For this purpose we recall...

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 59; no. 1
Main Authors Rybka, Piotr, Zatorska-Goldstein, Anna
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2020
Springer Nature B.V
Subjects
Analysis
Boundary conditions
Calculus of Variations and Optimal Control; Optimization
Conduction heating
Conductive heat transfer
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
28A33
35J20
35J70
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Summary:We study a basic linear elliptic equation on a lower dimensional rectifiable set S in R N with the Neumann boundary data. Set S is a support of a finite Borel measure μ . We will use the measure theoretic tools to interpret the equation and the Neumann boundary condition. For this purpose we recall the Sobolev-type space dependent on the measure μ . We establish existence and uniqueness of weak solutions provided that an appropriate source term is given.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-019-1695-9