Work

Regularity and existence for semilinear mixed local–nonlocal equations with variable singularities and measure data

Year: 2025

Type: article

Abstract: This paper proves the existence and regularity of weak solutions for a class of mixed local–nonlocal problems with singular nonlinearities. We examine both the purely singular problem and perturbed singular problems. A central contribution of this work is the inclusion of a variable singular exponent in the context of measure-valued data. Another notable feature is that the source terms in both the purely singular and perturbed components can simultaneously take the form of measures. To the best of our knowledge, this phenomenon is new, even in the case of a constant singular exponent.

Source: Communications in Contemporary Mathematics

DOI: 10.1142/s0219199725500282

Authors: Sanjit Biswas, Prashanta Garain

Institutions: Indian Institute of Technology Kanpur, Indian Institute of Science Education and Research Berhampur

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Indian Institute of Science Education and Research Mohali

OpenAlex ID: W4407149028

FWCI: 3.771

Cites: 37

Cited by: 2

Related to: 10