Displaying similar documents to “Generalized boundary value problems for nonlinear elliptic equations.”

Boundary trace of solutions of semilinear elliptic equalities and inequalities

Laurent Véron (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

The boundary trace problem for positive solutions of - △ ⁢ u + g ⁢ x , u ≥ 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.

Boundary trace of positive solutions of nonlinear elliptic inequalities

Moshe Marcus, Laurent Véron (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

We develop a new method for proving the existence of a boundary trace, in the class of Borel measures, of nonnegative solutions of - Δ u + g ( x , u ) ≥ 0 in a smooth domain Ω under very general assumptions on g . This new definition which extends the previous notions of boundary trace is based upon a sweeping technique by solutions of Dirichlet problems with measure boundary data. We also prove a boundary pointwise blow-up estimate of any solution of such inequalities in terms of the Poisson kernel. If the...