Geometric Estimates for Solutions of Semilinear Equations with Singular Potentials
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908858646003712 |
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| author | Nascimento, Thialita M. Zhang, Lei |
| author_facet | Nascimento, Thialita M. Zhang, Lei |
| contents | In this work, we study local minimizers of elliptic functionals with strong absorption terms and unbounded, sign-changing sources. These problems naturally interpolate between two classical free boundary problems: Bernoulli-type (cavity) and obstacle-type. While previous studies have focused on bounded and strictly positive sources, we extend sharp regularity and nondegeneracy estimates to the unbounded, sign-changing setting, providing a comprehensive analysis of how the underlying nonlinearity interacts with minimal integrability assumptions on the source. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00765 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric Estimates for Solutions of Semilinear Equations with Singular Potentials Nascimento, Thialita M. Zhang, Lei Analysis of PDEs 35J60, 35B65, 46E30 In this work, we study local minimizers of elliptic functionals with strong absorption terms and unbounded, sign-changing sources. These problems naturally interpolate between two classical free boundary problems: Bernoulli-type (cavity) and obstacle-type. While previous studies have focused on bounded and strictly positive sources, we extend sharp regularity and nondegeneracy estimates to the unbounded, sign-changing setting, providing a comprehensive analysis of how the underlying nonlinearity interacts with minimal integrability assumptions on the source. |
| title | Geometric Estimates for Solutions of Semilinear Equations with Singular Potentials |
| topic | Analysis of PDEs 35J60, 35B65, 46E30 |
| url | https://arxiv.org/abs/2603.00765 |