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

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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. 
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/
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     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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