Calculus of Variations and Geometric Measure Theory
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M. Eleuteri - P. Harjulehto - T. Lukkari

Global regularity and stability of solutions to elliptic equations with nonstandard growth

created by eleuteri on 15 Oct 2009
modified on 02 Dec 2013


Published Paper

Inserted: 15 oct 2009
Last Updated: 2 dec 2013

Journal: Complex Var. Elliptic Equ.
Volume: 56
Number: 7-9
Pages: 599-622
Year: 2011


We study the regularity properties of solutions to elliptic equations similar to the $\p$-Lap\-la\-cian. Our main results are a global reverse Hölder inequality, Hölder 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--Poincaré inequality, and a version of Hardy's inequality.

Keywords: Non standard growth, global higher integrability, stability of solutions, boundary regularity


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