Global Integrability for Minimizers of Obstacle Problems of Anisotropic Functionals

GAO Hongya, CUI Yi and LIANG S

Abstract

This paper deals with minimizers u ∈ K(pi) ψ,θ (Ω) of K (pi) ψ,θ -obstacle problems of anisotropic functionals whose prototype is Z Ω (|D1u| p1 + |D2u| p2 + · · · + |Dnu| pn ) dx. We show that higher integrability of θ∗ = max{θ, ψ} forces minimizers u to have higher integrability as well.