We find bilateral global bounds for the fundamental solutions associated with some quasilinear and fully nonlinear operators perturbed by a nonnegative zero order term with natural growth under minimal assumptions. Important model problems involve the equations , for , and , for . Here and are the -Laplace and -Hessian operators respectively, and is an arbitrary positive measurable function (or measure). We will in addition consider the Sobolev regularity of the fundamental solution away from its pole.
@article{ASNSP_2013_5_12_1_93_0, author = {Jaye, Benjamin J. and Verbitsky, Igor E.}, title = {The fundamental solution of nonlinear equations with natural growth terms}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {93--139}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 12}, number = {1}, year = {2013}, mrnumber = {3088438}, zbl = {1278.35095}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2013_5_12_1_93_0/} }
TY - JOUR AU - Jaye, Benjamin J. AU - Verbitsky, Igor E. TI - The fundamental solution of nonlinear equations with natural growth terms JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2013 SP - 93 EP - 139 VL - 12 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2013_5_12_1_93_0/ LA - en ID - ASNSP_2013_5_12_1_93_0 ER -
%0 Journal Article %A Jaye, Benjamin J. %A Verbitsky, Igor E. %T The fundamental solution of nonlinear equations with natural growth terms %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2013 %P 93-139 %V 12 %N 1 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2013_5_12_1_93_0/ %G en %F ASNSP_2013_5_12_1_93_0
Jaye, Benjamin J.; Verbitsky, Igor E. The fundamental solution of nonlinear equations with natural growth terms. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 1, pp. 93-139. http://www.numdam.org/item/ASNSP_2013_5_12_1_93_0/
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