Global gradient estimates for non-uniformly elliptic equations

Sun Sig Byun; Jehan Oh

doi:10.1007/s00526-017-1148-2

Global gradient estimates for non-uniformly elliptic equations

Sun Sig Byun, Jehan Oh

Seoul National University

Research output: Contribution to journal › Article › peer-review

69 Scopus citations

Abstract

We consider a nonlinear and non-uniformly elliptic problem in divergence form on a bounded domain. The problem under consideration is characterized by the fact that its ellipticity rate and growth radically change with the position, which provides a model for describing a feature of strongly anisotropic materials. We establish the global Calderón–Zygmund type estimates for the distributional solution in the case that the boundary of the domain is of class C¹ ^, ^β for some β> 0.

Original language	English
Article number	46
Journal	Calculus of Variations and Partial Differential Equations
Volume	56
Issue number	2
DOIs	https://doi.org/10.1007/s00526-017-1148-2
State	Published - 1 Apr 2017

Keywords

Primary 35J70
Secondary 35B65

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10.1007/s00526-017-1148-2

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AB - We consider a nonlinear and non-uniformly elliptic problem in divergence form on a bounded domain. The problem under consideration is characterized by the fact that its ellipticity rate and growth radically change with the position, which provides a model for describing a feature of strongly anisotropic materials. We establish the global Calderón–Zygmund type estimates for the distributional solution in the case that the boundary of the domain is of class C1 , β for some β> 0.

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Global gradient estimates for non-uniformly elliptic equations

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