Work

An elliptic problem involving critical Choquard and singular discontinuous nonlinearity

Year: 2025

Type: article

Abstract: The present article investigates the existence, multiplicity and regularity of weak solutions of problem involving a combination of critical Hartree-type nonlinearity along with singular and discontinuous nonlinearities (see ( P λ ) $\left({\mathcal{P}}_{\lambda }\right)$ below). 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 behaviour of weak solutions, we prove their Hölder and Sobolev regularity.

Source: Advanced Nonlinear Studies

DOI: 10.1515/ans-2023-0178

Authors: Gurdev Chand Anthal, Jacques Giacomoni, Konijeti Sreenadh