Boundary trace of solutions of semilinear elliptic equalities and inequalities

Laurent Véron

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2004)

  • Volume: 15, Issue: 3-4, page 301-314
  • ISSN: 1120-6330

Abstract

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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.

How to cite

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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 15.3-4 (2004): 301-314. <http://eudml.org/doc/252390>.

@article{Véron2004,
abstract = {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.},
author = {Véron, Laurent},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Laplacian; Poisson potential; Singularities; Radon measures; Borel measures; Convergence in measure; Balayage; singularities; balayage; convergence in measures},
language = {eng},
month = {12},
number = {3-4},
pages = {301-314},
publisher = {Accademia Nazionale dei Lincei},
title = {Boundary trace of solutions of semilinear elliptic equalities and inequalities},
url = {http://eudml.org/doc/252390},
volume = {15},
year = {2004},
}

TY - JOUR
AU - Véron, Laurent
TI - Boundary trace of solutions of semilinear elliptic equalities and inequalities
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/12//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 3-4
SP - 301
EP - 314
AB - 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.
LA - eng
KW - Laplacian; Poisson potential; Singularities; Radon measures; Borel measures; Convergence in measure; Balayage; singularities; balayage; convergence in measures
UR - http://eudml.org/doc/252390
ER -

References

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