An elliptic problem involving critical Choquard and singular discontinuous nonlinearity

2023/09/14 by Gurdev Chand Anthal, Jacques Giacomoni, Anthal, Gurdev C. +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2309.07542

openalex publication_date 2023/09/14 · openalex created_date 2023/09/16 · openalex updated_date 2026/07/28

Abstract

The present article investigates the existence, multiplicity and regularity of weak solutions of problems involving a combination of critical Hartree type nonlinearity along with singular and discontinuous nonlinearity. By applying variational methods and using the notion of generalized gradients for Lipschitz continuous functional, we obtain the existence and the multiplicity of weak solutions for some suitable range of λ and γ. Finally by studying the L^∞-estimates and boundary behavior of weak solutions, we prove their Hölder and Sobolev regularity.

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