Regularity theory for fully nonlinear equations of porous medium-type

2024/07/29 by Yun, Hyungsung
#35K55 #35K65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35B65 #Secondary 35D40

paper · doi:10.48550/arxiv.2407.20022

Abstract

In this paper, we establish the regularity results for nonnegative viscosity solutions to fully nonlinear equations of porous medium-type in bounded domains with the zero Dirichlet boundary condition, to be precise, we prove the global C^2,α-estimates of viscosity solutions. In many PDE problems, the C^2,α-estimates have been obtained through Schauder-type estimates. However, the Schauder-type estimates are not applicable to the porous medium-type equations. We provide techniques for handling porous medium-type equations so that the global C^2,α-estimates can be established.

Related

• Boundary Regularity for viscosity solutions of Fully nonlinear degenerate/singular parabolic equations
• Higher regularity estimates for the porous medium equation near the Heat\n equation
• Boundary regularity for viscosity solutions of fully nonlinear elliptic\n equations
• Optimal regularity and fine asymptotics for the porous medium equation in bounded domains
• Improved regularity for the porous medium equation along zero level-sets