The fundamental solution of nonlinear equations with natural growth terms
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 1, p. 93-139

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 -Δ p u=σu p-2 u+δ x 0 , for p>1, and F k (-u)=σu k-1 u+δ x 0 , for k1. Here Δ p and F k are the p-Laplace and k-Hessian operators respectively, and σ is an arbitrary positive measurable function (or measure). We will in addition consider the Sobolev regularity of the fundamental solution away from its pole.

Published online : 2019-02-21
Classification:  42B37,  31C45,  35J92,  42B25
@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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 12},
     number = {1},
     year = {2013},
     pages = {93-139},
     zbl = {1278.35095},
     mrnumber = {3088438},
     language = {en},
     url = {http://www.numdam.org/item/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, Serie 5, Volume 12 (2013) no. 1, pp. 93-139. http://www.numdam.org/item/ASNSP_2013_5_12_1_93_0/

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