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Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 5
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Articles

A quasilinear singular elliptic problem related to the Kardar–Parisi–Zhang equation

Pages 1096-1106 | Received 11 Mar 2019, Accepted 17 Jun 2019, Published online: 26 Jun 2019
 

ABSTRACT

In this paper, we will study existence and properties of solutions for the nonlinear Dirichlet problem div(M(x)u)=b(x)|u|uθ+f(x),in Ω,u=0,on Ω, where ΩRN is a bounded domain, 0<θ1, M is a uniformly elliptic and bounded matrix, and b, f are functions in some Lebesgue spaces.

2010 Mathematics Subject Classifications:

Acknowledgements

Part of this work has been carried out during the stays of the first author at the Departamento de Matemàticas of Universidad Autónoma de Madrid and at the ‘Dipartimento di chirurgia generale e specialistica’ of Sapienza for a cooperation with Professor Massimo Rossi. We also thank the referee for the useful remarks on the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is done with the support of the projects MTM2013-40846-P and MTM2016-80474-P, Spain.

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