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

2024/08/19 by Gurdev Chand Anthal, Anthal, Gurdev Chand, Prashanta Garain +1 · 2 citations
Mathematics · #35B06 #35B25 #35B65 #35J75 #35M10 #35R11 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2408.09924

openalex publication_date 2024/08/19 · openalex created_date 2024/09/13 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Mixed local-nonlocal p-Laplace equation with variable singular nonlinearity in the Heisenberg group
• Existence Theory for a class of semilinear mixed local and nonlocal equations involving variable singularities and singular measures

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