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arXiv · 2602.19054

Symmetry and Approximate Symmetry for Solutions of Mixed Local-Nonlocal Singular Equations

Sanjit Biswas
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Abstract

In this article, we establish radial symmetry for positive weak solutions of a class of mixed local-nonlocal equations with possibly singular nonlinearity via the moving plane method. Furthermore, we provide a quantitative version of Gidas-Ni-Nirenberg type theorem for mixed local-nonlocal equations. In this regard, we establish a weak Harnack-type inequality and an analogue of the Alexandroff-Bakelman-Pucci inequality in the mixed nonhomogeneous setting with a lower order term, which appear to be new. To the best of our knowledge, this paper initiates the study of the quantitative properties of solutions to mixed problems.

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Sanjit Biswas. 2026-02-22. Symmetry and Approximate Symmetry for Solutions of Mixed Local-Nonlocal Singular Equations. https://arxiv.org/abs/2602.19054

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