We study the regularity properties of solutions to elliptic equations similar to the p(·)-Laplacian. Our main results are a global reverse H¨older inequality, H¨older continuity up to the boundary, and stability of solutions with respect to continuous perturbations in the variable growth exponent. We assume that the complement of the domain is uniformly fat in a capacitary sense. As technical tools, we derive a capacitary Sobolev–Poincar´e inequality, and a version of Hardy’s inequality
Global regularity and stability of solutions to elliptic equations with nonstandard growth / Eleuteri, Michela; Harjulehto, Petteri; Lukkari, Teemu. - In: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS. - ISSN 1747-6933. - 56:7-9(2011), pp. 599-622. [10.1080/17476930903568399]
Global regularity and stability of solutions to elliptic equations with nonstandard growth
ELEUTERI, Michela;
2011
Abstract
We study the regularity properties of solutions to elliptic equations similar to the p(·)-Laplacian. Our main results are a global reverse H¨older inequality, H¨older continuity up to the boundary, and stability of solutions with respect to continuous perturbations in the variable growth exponent. We assume that the complement of the domain is uniformly fat in a capacitary sense. As technical tools, we derive a capacitary Sobolev–Poincar´e inequality, and a version of Hardy’s inequality
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