Symmetry, existence and regularity results for a class of mixed local-nonlocal semilinear singular elliptic problem via variational characterization

Fuente: arXiv
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Main Authors: Anthal, Gurdev Chand, Garain, Prashanta
Format: Preprint
Published: 2024
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_version_ 1866910990646378496
author Anthal, Gurdev Chand
Garain, Prashanta
author_facet Anthal, Gurdev Chand
Garain, Prashanta
contents In this article, we present the symmetry of weak solutions to a mixed local-nonlocal singular problem. We also establish results related to the existence, nonexistence, and regularity of weak solutions to a mixed local-nonlocal singular jumping problem. A crucial element in proving our main results is the variational characterization of the solutions, which also reveals the decomposition property. This decomposition property, together with comparison principles and the moving plane method, yields the symmetry result. Additionally, we utilize nonsmooth critical point theory alongside the variational characterization to analyze the jumping problem.
format Preprint
id arxiv_https___arxiv_org_abs_2408_09924
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Symmetry, existence and regularity results for a class of mixed local-nonlocal semilinear singular elliptic problem via variational characterization
Anthal, Gurdev Chand
Garain, Prashanta
Analysis of PDEs
35M10, 35J75, 35B06, 35B25, 35B65, 35R11
In this article, we present the symmetry of weak solutions to a mixed local-nonlocal singular problem. We also establish results related to the existence, nonexistence, and regularity of weak solutions to a mixed local-nonlocal singular jumping problem. A crucial element in proving our main results is the variational characterization of the solutions, which also reveals the decomposition property. This decomposition property, together with comparison principles and the moving plane method, yields the symmetry result. Additionally, we utilize nonsmooth critical point theory alongside the variational characterization to analyze the jumping problem.
title Symmetry, existence and regularity results for a class of mixed local-nonlocal semilinear singular elliptic problem via variational characterization
topic Analysis of PDEs
35M10, 35J75, 35B06, 35B25, 35B65, 35R11
url https://arxiv.org/abs/2408.09924