Geodesic
Boundary trace of solutions of semilinear elliptic equalities and inequalities
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 15 (2004) no. 3-4, pp. 301-314 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
@article{RLIN_2004_9_15_3-4_a11,
     author = {V\'eron, Laurent},
     title = {Boundary trace of solutions of semilinear elliptic equalities and inequalities},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {301--314},
     year = {2004},
     volume = {Ser. 9, 15},
     number = {3-4},
     zbl = {1113.35075},
     mrnumber = {MR2148887},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2004_9_15_3-4_a11/}
}
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Véron, Laurent. Boundary trace of solutions of semilinear elliptic equalities and inequalities. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 15 (2004) no. 3-4, pp. 301-314. http://geodesic.mathdoc.fr/item/RLIN_2004_9_15_3-4_a11/