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arXiv · 2603.00765

Geometric Estimates for Solutions of Semilinear Equations with Singular Potentials

Thialita M. Nascimento·Lei Zhang
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Abstract

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.

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Thialita M. Nascimento, Lei Zhang. 2026-02-28. Geometric Estimates for Solutions of Semilinear Equations with Singular Potentials. https://arxiv.org/abs/2603.00765

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