Hölder regularity for non-variational porous media type equations

Héctor A. Chang-Lara; Makson S. Santos

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arXiv · 2108.00464

Hölder regularity for non-variational porous media type equations

Héctor A. Chang-Lara·Makson S. Santos

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Abstract

We present a Krylov-Safonov theory approach for the Hölder regularity of viscosity solutions to non-variational porous media type equations. We explore the peculiarity of this type of problem: either the equation falls in a uniformly elliptic regime or the eikonal mechanism takes care of the regularity. Our techniques are based on sliding paraboloids resulting in an ABP-type measure estimate. By combining such estimates, a diminishing of oscillation property is available, resulting in a regularity control in Hölder spaces.

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Héctor A. Chang-Lara, Makson S. Santos. 2022-09-14. Hölder regularity for non-variational porous media type equations. https://arxiv.org/abs/2108.00464

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