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.

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 $-{\Delta }_{p}u=\sigma {\left|u\right|}^{p-2}u+{\delta }_{{x}_{0}}$, for $p>1$, and ${F}_{k}\left(-u\right)=\sigma {\left|u\right|}^{k-1}u+{\delta }_{{x}_{0}}$, for $k\ge 1$. Here ${\Delta }_{p}$ and ${F}_{k}$ are the $p$-Laplace and $k$-Hessian operators respectively, and $\sigma$ is an arbitrary positive measurable function (or measure). We will in addition consider the Sobolev regularity of the fundamental solution away from its pole.

Publié le : 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},
pages = {93--139},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 12},
number = {1},
year = {2013},
zbl = {1278.35095},
mrnumber = {3088438},
language = {en},
url = {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, 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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