Mathematica Eterna
Open Access

Abstract

Regularity for Minimizers to Anisotropic Integrals Functions with Nonstandard Growth

Miaomiao JIA

In this paper we deal with the problem u ∈ Cψ(Ω), ∀ ω ∈ Cψ(Ω), Z Ω f(x, Du)dx ≤ Z Ω f(x, Dω)dx, where Cψ(Ω) = {w ∈ u∗ + W 1,(pi) 0 (Ω) such that x → f(x, Dw) ∈ L 1 (Ω), w ≥ ψ, a.e. Ω}. We consider a minimizer u : Ω ⊂ Rn → R among all functions that agree on the boundary ∂Ω with some fixed boundary value u∗. And we assume that the function θ = max{u∗, ψ} makes the density f(x, Du) more integrable under the obstacle problem and we prove that the minimizer u enjoy higher integrability.