Existence Theory for a class of semilinear mixed local and nonlocal equations involving variable singularities and singular measures

2025/07/06 by Biswas, Sanjit, Garain, Prashanta · 1 citation
#35J75 #35M10 #35M12 #35R06 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.04260

Abstract

This article establishes the existence of weak solutions for a class of mixed local-nonlocal problems with pure and perturbed singular nonlinearities. A key novelty is the treatment of variable singular exponents alongside measure-valued data. Notably, both source terms may be measures, with the singular component modeled by both a singular and non-singular measure. Our main focus is on the singular measure data, which appears to be new, even for constant exponents.

Citations

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Cited by

• Regularity and existence for a mixed local-nonlocal parabolic equation with variable singularities and measure data

Related

• Regularity and existence for a mixed local-nonlocal parabolic equation with variable singularities and measure data
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• On the regularity theory for mixed anisotropic and nonlocal p-Laplace equations and its applications to singular problems
• Symmetry and Approximate Symmetry for Solutions of Mixed Local-Nonlocal Singular Equations
• Existence results for mixed local and nonlocal elliptic equations involving singularity and nonregular data