Some Aspects of the Boundary Trace Problem for Solutions of Nonlinear Elliptic Equations

L. Véron

Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 1, Tome 1 (2003), pp. 56-68.

Résumé

The boundary trace problem for positive solutions of $-\mathrm{\Delta }u+g(x,u)=0$ is considered for a large class of nonlinearities and three different methods for defining the trace are compared. The boundary trace is usually a generalized Borel measure. The associated Dirichlet problem with boundary data in the set of such Borel measures is studied.

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