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.

Weighted L^p-estimates for elliptic equations with measurable coefficients in nonsmooth domains / Byun, S. S.; Palagachev, Dian Kostadinov. - In: POTENTIAL ANALYSIS. - ISSN 0926-2601. - 41:1(2014), pp. 51-79. [10.1007/s11118-013-9363-8]

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

PALAGACHEV, Dian Kostadinov
2014-01-01

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.
2014
Weighted L^p-estimates for elliptic equations with measurable coefficients in nonsmooth domains / Byun, S. S.; Palagachev, Dian Kostadinov. - In: POTENTIAL ANALYSIS. - ISSN 0926-2601. - 41:1(2014), pp. 51-79. [10.1007/s11118-013-9363-8]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/6658
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