Mathematica Eterna
Open Access

Abstract

Regularity of Weak Solutions to Some Anisotropic Elliptic Equations

GAO Yanmin and GAO Hongya

We consider boundary value problem of the form    Pn i=1 Di(ai(x, Du(x))) = f, x ∈ Ω, u(x) = u∗(x), x ∈ ∂Ω. We show that regularity of boundary datum u∗ forces u to have regularity as well. A similar result is obtained for obstacle problem.