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 -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.

Publié le :
Classification : 42B37, 31C45, 35J92, 42B25
Jaye, Benjamin J. 1 ; Verbitsky, Igor E. 1

1 Department of Mathematics University of Missouri 202 Mathematical Sciences Bldg Columbia, Missouri 65211, USA
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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://archive.numdam.org/item/ASNSP_2013_5_12_1_93_0/

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