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Global Integrability for Minimizers of Obstacle Problems of Anisotropic Functionals

GAO Hongya, CUI Yi and LIANG Shuang

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.