Véron: Boundary trace of solutions of semilinear elliptic equalities and inequalities

Véron, Laurent:
Boundary trace of solutions of semilinear elliptic equalities and inequalities
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 15 (2004), fasc. n.3-4, p. 301-314, (English)
pdf (277 Kb), djvu (192 Kb). | MR2148887 | Zbl 1113.35075

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The boundary trace problem for positive solutions of $$-\triangle u + g(x ,u) \ge 0$$ is considered for nonlinearities of absorption type, and three different methods for defining the trace are compared. The boundary trace is obtained as a generalized Borel measure. The associated Dirichlet problem with boundary data in the set of such Borel measures is studied.

Referenze Bibliografiche

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