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arXiv · 2302.00423

Regularity estimates for fully nonlinear integro-differential equations with nonhomogeneous degeneracy

Pêdra D. S. Andrade·Disson S. dos Prazeres·Makson S. Santos
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Abstract

We investigate the regularity of the solutions for a class of degenerate/singular fully nonlinear nonlocal equations. In the degenerate scenario, we establish that there exists at least one viscosity solution of class $C_{loc}^{1, \alpha}$, for some constant $\alpha \in (0, 1)$. In addition, under suitable conditions on $\sigma$, we prove regularity estimates in H\"older spaces for any viscosity solution. We also examine the singular setting and prove H\"older regularity estimates for the gradient of the solutions.

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Pêdra D. S. Andrade, Disson S. dos Prazeres, Makson S. Santos. 2023-02-01. Regularity estimates for fully nonlinear integro-differential equations with nonhomogeneous degeneracy. https://arxiv.org/abs/2302.00423

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