Liouville type theorems and regularity of solutions to degenerate or singular problems part I: even solutions

We consider a class of equations in divergence form with a singular/degenerate weight Under suitable regularity assumptions for the matrix A and f (resp. F) we prove Hölder continuity of solutions which are even in and possibly of their derivatives up to order two or more (Schauder estimates). In ad...

Full description

Saved in:
Bibliographic Details
Published inCommunications in partial differential equations Vol. 46; no. 2; pp. 310 - 361
Main Authors Sire, Yannick, Terracini, Susanna, Vita, Stefano
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 01.02.2021
Taylor & Francis Ltd
Subjects
blow-up
Continuity (mathematics)
Degenerate and singular elliptic equations
fractional divergence form elliptic operator
fractional Laplacian
Liouville type theorems
Regularity
Schauder estimates
Theorems
Online AccessGet full text

Cover

More Information
Summary:We consider a class of equations in divergence form with a singular/degenerate weight Under suitable regularity assumptions for the matrix A and f (resp. F) we prove Hölder continuity of solutions which are even in and possibly of their derivatives up to order two or more (Schauder estimates). In addition, we show stability of the and a priori bounds for approximating problems in the form as Finally, we derive and bounds for inhomogenous Neumann boundary problems as well. Our method is based upon blow-up and appropriate Liouville type theorems.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2020.1840586