Symmetry and Approximate Symmetry for Solutions of Mixed Local-Nonlocal Singular Equations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911461410865152 |
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| author | Biswas, Sanjit |
| author_facet | Biswas, Sanjit |
| contents | 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. To 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19054 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetry and Approximate Symmetry for Solutions of Mixed Local-Nonlocal Singular Equations Biswas, Sanjit Analysis of PDEs 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. To 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. |
| title | Symmetry and Approximate Symmetry for Solutions of Mixed Local-Nonlocal Singular Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.19054 |