A doubly nonlinear elliptic problem with variable exponents, homogeneous Neumann conditions and generalized logistic source

Fuente: arXiv
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Main Author: Maxim, Bogdan
Format: Preprint
Published: 2025
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_version_ 1866912457539190784
author Maxim, Bogdan
author_facet Maxim, Bogdan
contents The aim of this work is to prove existence and uniqueness results for a doubly nonlinear elliptic problem that is essential for solving the associated parabolic problem using Rothe's method (discretizing time). We work under very weak assumptions, dropping the commonly used condition that the source term is locally Lipschitz, which appears frequently in the literature. Instead, we rely on the continuity of the Nemytskii operator between two Lebesgue spaces with variable exponents. All results presented here are proved in full detail, which makes the article lengthy.
format Preprint
id arxiv_https___arxiv_org_abs_2506_23660
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A doubly nonlinear elliptic problem with variable exponents, homogeneous Neumann conditions and generalized logistic source
Maxim, Bogdan
Analysis of PDEs
35A01, 35A02, 35B09, 35D30, 35J20, 35J62, 35J92, 98A08
The aim of this work is to prove existence and uniqueness results for a doubly nonlinear elliptic problem that is essential for solving the associated parabolic problem using Rothe's method (discretizing time). We work under very weak assumptions, dropping the commonly used condition that the source term is locally Lipschitz, which appears frequently in the literature. Instead, we rely on the continuity of the Nemytskii operator between two Lebesgue spaces with variable exponents. All results presented here are proved in full detail, which makes the article lengthy.
title A doubly nonlinear elliptic problem with variable exponents, homogeneous Neumann conditions and generalized logistic source
topic Analysis of PDEs
35A01, 35A02, 35B09, 35D30, 35J20, 35J62, 35J92, 98A08
url https://arxiv.org/abs/2506.23660