We consider the Dirichlet problem for positive solutions of the equation $-Delta_p (u) = f(u)$ in a convex, bounded, smooth domain $Omega subsetR^N$, with $f$ locally Lipschitz continuous. par We provide sufficient conditions guarantying $L^{infty} $ a priori bounds for positive solutions of some elliptic equations involving the $p$-Laplacian and extend the class of known nonlinearities for which the solutions are $L^{infty} $ a priori bounded. As a consequence we prove the existence of positive solutions in convex bounded domains.

Damascelli, L., & Pardo, R. (2018). A priori estimates for some elliptic equations involving the $p$-laplacian. NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS, 41, 475-496 [10.1016/j.nonrwa.2017.11.003].

A priori estimates for some elliptic equations involving the $p$-laplacian

Damascelli Lucio;
2018

Abstract

We consider the Dirichlet problem for positive solutions of the equation $-Delta_p (u) = f(u)$ in a convex, bounded, smooth domain $Omega subsetR^N$, with $f$ locally Lipschitz continuous. par We provide sufficient conditions guarantying $L^{infty} $ a priori bounds for positive solutions of some elliptic equations involving the $p$-Laplacian and extend the class of known nonlinearities for which the solutions are $L^{infty} $ a priori bounded. As a consequence we prove the existence of positive solutions in convex bounded domains.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - Analisi Matematica
English
Con Impact Factor ISI
A priori estimates, quasilinear elliptic equations with $p$-Laplacian, critical Sobolev esponent, moving planes method, Pohozaev identitysep Picone identity, positive solutions.
Damascelli, L., & Pardo, R. (2018). A priori estimates for some elliptic equations involving the $p$-laplacian. NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS, 41, 475-496 [10.1016/j.nonrwa.2017.11.003].
Damascelli, L; Pardo, R
Articolo su rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/191059
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