A regularity result for nonuniformly elliptic equations with lower order terms
Volume 276 / 2024
Studia Mathematica 276 (2024), 1-17
MSC: Primary 35B65; Secondary 35J60, 49N60
DOI: 10.4064/sm230104-18-3
Published online: 4 June 2024
Abstract
This paper is about the higher differentiability of solutions to the Dirichlet problem $$ \begin{cases} \textrm{div} (A(x, Du)) + b(x)u(x)=f &\text{in}\ \Omega ,\\ u=0 &\text{on}\ \partial \Omega , \end{cases}$$ under a Sobolev assumption on the partial map $x \mapsto A(x, \xi )$. The novelty here is that we consider a nonuniformly elliptic operator and we take advantage of the regularizing effect of the lower order term to deal with bounded solutions.
