Mathematica Eterna
Open Access

Abstract

Regularity for Minimizers of Some Anisotropic Integral Functionals with Nonstandard Growth

Guo Qiannan and Gao Hongya

This paper deals with anisotropic integral functionals of the type I(u) = Z Ω f(x, Du(x))dx, where the Carath´eodory function f(x, z) : Ω × R n → R satisfies the growth condition µ Xn i=1 |zi | pi − g(x) ≤ f(x, z) for almost every x ∈ Ω and all z ∈ R n . We consider a minimizer u : Ω ∈ R n → R among all functions that agree on the boundary ∂Ω with some fixed boundary value u∗ and with gradient constraints. We assume that the boundary datum u∗ make the density f(x, Du∗(x)) more integrable and we prove that the minimizer u enjoys higher integrability.