We develop a new method for proving the existence of a boundary trace, in the class of Borel measures, of nonnegative solutions of in a smooth domain under very general assumptions on . 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 , we exhibit a new full boundary blow-up phenomenon.
@article{ASNSP_2004_5_3_3_481_0, author = {Marcus, Moshe and V\'eron, Laurent}, title = {Boundary trace of positive solutions of nonlinear elliptic inequalities}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {481--533}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 3}, number = {3}, year = {2004}, mrnumber = {2099247}, zbl = {1121.35057}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2004_5_3_3_481_0/} }
TY - JOUR AU - Marcus, Moshe AU - Véron, Laurent TI - Boundary trace of positive solutions of nonlinear elliptic inequalities JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2004 SP - 481 EP - 533 VL - 3 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2004_5_3_3_481_0/ LA - en ID - ASNSP_2004_5_3_3_481_0 ER -
%0 Journal Article %A Marcus, Moshe %A Véron, Laurent %T Boundary trace of positive solutions of nonlinear elliptic inequalities %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2004 %P 481-533 %V 3 %N 3 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2004_5_3_3_481_0/ %G en %F ASNSP_2004_5_3_3_481_0
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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