Boundary trace of positive solutions of nonlinear elliptic inequalities
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 3, pp. 481-533.

We develop a new method for proving the existence of a boundary trace, in the class of Borel measures, of nonnegative solutions of -Δu+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 nonlinearity is very degenerate near the boundary, for example if g(x,u)exp(-ρ Ω -1 (x))u q , we exhibit a new full boundary blow-up phenomenon.

Classification: 35K60
Marcus, Moshe 1; Véron, Laurent 2

1 Department of Mathematics, Israel Institute of Technology Technion, Haifa 32000, Israel
2 Université François Rabelais Tours 37200, France
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Marcus, Moshe; Véron, Laurent. Boundary trace of positive solutions of nonlinear elliptic inequalities. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 3, pp. 481-533. http://archive.numdam.org/item/ASNSP_2004_5_3_3_481_0/

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