We study fully nonlinear elliptic equations such as
in or in exterior domains, where is any uniformly elliptic, positively homogeneous operator. We show that there exists a critical exponent, depending on the homogeneity of the fundamental solution of , that sharply characterizes the range of for which there exist positive supersolutions or solutions in any exterior domain. Our result generalizes theorems of Bidaut-Véron [6] as well as Cutri and Leoni [11], who found critical exponents for supersolutions in the whole space , in case is Laplace’s operator and Pucci’s operator, respectively. The arguments we present are new and rely only on the scaling properties of the equation and the maximum principle.
@article{ASNSP_2011_5_10_3_729_0, author = {Armstrong, Scott N. and Sirakov, Boyan}, title = {Sharp {Liouville} results for fully nonlinear equations with power-growth nonlinearities}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {729--746}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 10}, number = {3}, year = {2011}, mrnumber = {2905384}, zbl = {1250.35050}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2011_5_10_3_729_0/} }
TY - JOUR AU - Armstrong, Scott N. AU - Sirakov, Boyan TI - Sharp Liouville results for fully nonlinear equations with power-growth nonlinearities JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2011 SP - 729 EP - 746 VL - 10 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2011_5_10_3_729_0/ LA - en ID - ASNSP_2011_5_10_3_729_0 ER -
%0 Journal Article %A Armstrong, Scott N. %A Sirakov, Boyan %T Sharp Liouville results for fully nonlinear equations with power-growth nonlinearities %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2011 %P 729-746 %V 10 %N 3 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2011_5_10_3_729_0/ %G en %F ASNSP_2011_5_10_3_729_0
Armstrong, Scott N.; Sirakov, Boyan. Sharp Liouville results for fully nonlinear equations with power-growth nonlinearities. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 3, pp. 729-746. http://www.numdam.org/item/ASNSP_2011_5_10_3_729_0/
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