H?lder regularity for non-variational porous media type equations

被引：0

作者：

Chang-Lara, Hector A. ^{[1
]}

Santos, Makson S. ^{[1
]}

机构：

[1] CIMAT, Dept Math, Guanajuato, Mexico

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 360卷

关键词：

Porous media; Krylov-Safonov theory; H?lder estimates; Degenerate parabolic equations; ABP principle; VISCOSITY SOLUTIONS; WEAK SOLUTIONS; PARABOLIC EQUATIONS; FREE-BOUNDARY; GAS-FLOW; CONTINUITY; DEGENERATE; DIFFUSION;

D O I：

10.1016/j.jde.2023.02.055

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a Krylov-Safonov theory approach for the Holder regularity of viscosity solutions to nonvariational 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 Holder spaces. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：347 / 372

页数：26

共 38 条

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