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arXiv · 2605.02562

The obstacle problem for singular quasi-linear elliptic equations

Annamaria Barbagallo·Umberto Guarnotta
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Abstract

Existence of solutions to an obstacle $p$-Laplacian problem exhibiting a singular, discontinuous reaction is proved. The reaction term may be discontinuous in a Lebesgue-negligible set. Moreover, solutions are shown to be locally $C^{1,\alpha}$ far away from the contact set. Under a differentiability hypothesis on the obstacle, solutions belong to $C^{1,\alpha}(\overline{\Omega})$.

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Annamaria Barbagallo, Umberto Guarnotta. 2026-05-04. The obstacle problem for singular quasi-linear elliptic equations. https://arxiv.org/abs/2605.02562

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