Inserted: 15 oct 2009
Last Updated: 2 dec 2013
Journal: Complex Var. Elliptic Equ.
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