We study the generalized boundary value problem for nonnegative solutions of in a bounded Lipschitz domain , when is continuous and nondecreasing. Using the harmonic measure of , we define a trace in the class of outer regular Borel measures. We amphasize the case where , . When is (locally) a cone with vertex , we prove sharp results of removability and characterization of singular behavior. In the general case, assuming that possesses a tangent cone at every boundary point and is subcritical, we prove an existence and uniqueness result for positive solutions with arbitrary boundary trace.
@article{ASNSP_2011_5_10_4_913_0, author = {Marcus, Moshe and Veron, Laurent}, title = {Boundary trace of positive solutions of semilinear elliptic equations in {Lipschitz} domains: the subcritical case}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {913--984}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 10}, number = {4}, year = {2011}, mrnumber = {2932897}, zbl = {1243.35054}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2011_5_10_4_913_0/} }
TY - JOUR AU - Marcus, Moshe AU - Veron, Laurent TI - Boundary trace of positive solutions of semilinear elliptic equations in Lipschitz domains: the subcritical case JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2011 SP - 913 EP - 984 VL - 10 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2011_5_10_4_913_0/ LA - en ID - ASNSP_2011_5_10_4_913_0 ER -
%0 Journal Article %A Marcus, Moshe %A Veron, Laurent %T Boundary trace of positive solutions of semilinear elliptic equations in Lipschitz domains: the subcritical case %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2011 %P 913-984 %V 10 %N 4 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2011_5_10_4_913_0/ %G en %F ASNSP_2011_5_10_4_913_0
Marcus, Moshe; Veron, Laurent. Boundary trace of positive solutions of semilinear elliptic equations in Lipschitz domains: the subcritical case. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 4, pp. 913-984. http://archive.numdam.org/item/ASNSP_2011_5_10_4_913_0/
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