Hölder Continuity for Solutions of Linear Degenerate Elliptic Equations Under Minimal Assumptions
By P. Zamboni. 2002
57 citations recorded by the source corpus.
Abstract In this paper, we study the local regularity of solutions to linear degenerate elliptic equations of the form − ∑ i, j=1 n (a ij u x i +d j u) x j + ∑ i=1 n b i u x i +cu=f− ∑ i=1 n (f i ) x i . ((*)) We prove Harnack's inequality for positive solutions and the Holder continuity of the solutions of (*), assuming on the coefficients of the lower order terms very general hypotheses involving appropriate “degenerate” Morrey spaces.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3e367b95290cb7a1857f419dba7d0fb4f6467929
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In Applied Mathematics
- M. Kassmann
- Pablo Raúl Stinga
- Xavier Ros-Oton
- Luis Silvestre
- Matteo Cozzi
- C. Imbert
- Bartłomiej Dyda
- Juan Luis V'azquez
In Mathematical Physics
- M. Kassmann
- Pablo Raúl Stinga
- Xavier Ros-Oton
- Luis Silvestre
- Bartłomiej Dyda
- Juan Luis V'azquez
- Matteo Cozzi
- Russell W. Schwab
Citations in the corpus
- Harnack Inequalities: An Introduction (2007, background): “Degenerate elliptic operators: [67] establishes a Harnack inequality, [68] investigates Green’s functions; [69, 70] allow for different new kinds of weights; [71] studies X-elliptic operators; [72] further relaxes assumptions on the weights and allows for terms of lower order; [73] investigates quit”