Boundary trace of positive solutions of semilinear elliptic equations in Lipschitz domains

Abstract

We study the generalized boundary value problem for nonnegative solutions of of −∆u + g(u) = 0 in a bounded Lipschitz domain Ω, when g is continuous and nondecreasing. Using the harmonic measure of Ω, we define a trace in the class of outer regular Borel measures. We amphasize the case where g(u) = |u|q−1u, q > 1. When Ω is (locally) a cone with vertex y… (More)

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