On the regularity and existence of weak solutions for a class of degenerate singular elliptic problem

2021/10/22 by Prashanta Garain, Garain, Prashanta · 3 citations
Computer Science · Mathematics · #35D30 #35J70 #35J75 #35J92 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2110.12049

openalex publication_date 2021/10/22 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In this article, we consider a class of degenerate singular problems. The degeneracy is captured by the presence of a class of p-admissible weights, which may vanish or blow up near the origin. Further, the singularity is allowed to vary inside the domain. We provide sufficient conditions on the weight function, on the singular exponent and the source function to establish regularity and existence results.

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• Mixed local-nonlocal p-Laplace equation with variable singular nonlinearity in the Heisenberg group
• Nonlocal singular problem and associated Sobolev type inequality with extremal 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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