This paper is about the higher differentiability of solutions to the Dirichlet problem $div (A(x, Du)) + b(x)u(x)=f$ in \Omega$ and $u=0$ on $\partial \Omega$ under a Sobolev assumption on the partial map $x \rightarrow A(x, \xi)$. The novelty here is that we consider nonuniformly elliptic operator and we take advantage from the regularizing effect of the lower order term to deal with bounded solutions.
A regularity result for nonuniformly elliptic equations with lower order terms / Radice, Teresa. - In: STUDIA MATHEMATICA. - ISSN 0039-3223. - 276:1(2024), pp. 1-17. [10.4064/sm230104-18-3]
A regularity result for nonuniformly elliptic equations with lower order terms
Teresa Radice
2024
Abstract
This paper is about the higher differentiability of solutions to the Dirichlet problem $div (A(x, Du)) + b(x)u(x)=f$ in \Omega$ and $u=0$ on $\partial \Omega$ under a Sobolev assumption on the partial map $x \rightarrow A(x, \xi)$. The novelty here is that we consider nonuniformly elliptic operator and we take advantage from the regularizing effect of the lower order term to deal with bounded solutions.File in questo prodotto:
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