Boundary trace of positive solutions of semilinear elliptic equations in Lipschitz domains: the subcritical case
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 4, pp. 913-984.

We study the generalized boundary value problem for nonnegative solutions of -Δu+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-1 u, q>1. When Ω is (locally) a cone with vertex y, we prove sharp results of removability and characterization of singular behavior. In the general case, assuming that Ω possesses a tangent cone at every boundary point and q is subcritical, we prove an existence and uniqueness result for positive solutions with arbitrary boundary trace.

Published online:
Classification: 35K60, 31A20, 31C15, 44A25, 46E35
Marcus, Moshe 1; Veron, Laurent 2

1 Department of Mathematics Technion Haifa, Israel
2 Laboratoire de Mathématiques Faculté des Sciences Parc de Grandmont 37200 Tours, France
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Marcus, Moshe; Veron, Laurent. Boundary trace of positive solutions of semilinear elliptic equations in Lipschitz domains: the subcritical case. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 4, pp. 913-984. http://archive.numdam.org/item/ASNSP_2011_5_10_4_913_0/

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