In this paper we establish the higher differentiability of solutions to the Dirichlet problem $div (A(x, Du)) + b(x)u(x)=f$ in $Omega$ with u=0 on $partial Omega$under a Sobolev assumption on the partial map $x ightarrow A(x, \xi)$. The novelty here is that we take advantage from the regularizing effect of the lower order term to deal with bounded solutions.
A regularity result for a class of elliptic equations with lower order terms / Capone, Claudia; Radice, Teresa. - In: JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS. - ISSN 2296-9020. - 6:2(2020), pp. 751-771. [10.1007/s41808-020-00082-w]
A regularity result for a class of elliptic equations with lower order terms
Teresa Radice
2020
Abstract
In this paper we establish the higher differentiability of solutions to the Dirichlet problem $div (A(x, Du)) + b(x)u(x)=f$ in $Omega$ with u=0 on $partial Omega$under a Sobolev assumption on the partial map $x ightarrow A(x, \xi)$. The novelty here is that 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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