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Global gradient estimates for elliptic equations of <i>p</i>(<i>x</i>)-Laplacian type with BMO nonlinearity
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2014
Year
Elliptic EquationEngineeringBounded DomainLipschitz CategoryGlobal Gradient Estimates-Laplacian TypeBmo NonlinearityFunctional AnalysisNonlinear Functional AnalysisNonlinear Elliptic ProblemVariational InequalitiesElliptic Function
Abstract We consider a nonlinear elliptic problem in divergence form, with nonstandard growth conditions, on a bounded domain. We obtain the global Calderón–Zygmund type gradient estimates for the weak solution of such a problem in the setting of Lebesgue and Sobolev spaces with variable p ( x ) exponents, in the case that the nonlinearity of the coefficients is allowed to be discontinuous and the domain goes beyond the Lipschitz category. We assume that the nonlinearity has small BMO semi-norms and the boundary of the domain satisfies the so-called δ-Reifenberg flatness condition. These conditions on the nonlinearity and the boundary are weaker than those reported in other studies in the literature.