Mathematica Eterna
Open Access

Abstract

Regularity for Solutions to Obstacle Problems of Some Anisotropic Elliptic Systems

Gao Hongya and Gao Yanmin

This paper deals with K (pi) ψ,θ -obstacle problems of the system of N partial differential equations Xn i=1 Di(a α i (x, Du(x))) = Xn i=1 DiF α i (x), α = 1, · · · N. We show that, for any fixed β ∈ {1, · · · , N}, higher integrability of the datum θ β ∗ = max{ψ β , θβ} forces the component u β of solutions u to have higher integrability as well, provided we assume suitable ellipticity and growth conditions on a α i .