Weighted L^p-estimates for elliptic equations with measurable coefficients in nonsmooth domains

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Abstract

We obtain a global weighted $L^p$ estimate for the gradient of the weak solutions to divergence form elliptic equations with measurable coefficients in a nonsmooth bounded domain. The coefficients are assumed to be merely measurable in one variable and to have small BMO semi-norms in the remaining variables, while the boundary of the domain is supposed to be Reifenberg flat, which goes beyond the category of domains with Lipschitz continuous boundaries. As consequence of the main result, we derive global gradient estimate for the weak solution in the framework of the Morrey spaces which implies global H"older continuity of the solution."

Autore Pugliese

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  • BYUN S.-S. , PALAGACHEV D.K.

Titolo volume/Rivista

POTENTIAL ANALYSIS

Anno di pubblicazione

2014

ISSN

0926-2601

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

9

Ultimo Aggiornamento Citazioni

2017-04-22 03:20:59

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile