Optimal boundary regularity for fast diffusion equations in bounded domains
Tianling Jin, Jingang Xiong
Abstract
We prove optimal boundary regularity for bounded positive weak solutions of fast diffusion equations in smooth bounded domains. This solves a problem raised by Berryman and Holland in 1980 for these equations in the subcritical and critical regimes. Our proof of the a priori estimates uses a geometric type structure of the fast diffusion equations, where an important ingredient is an evolution equation for a curvature-like quantity.
Topics & Concepts
Bounded functionMathematicsA priori and a posterioriBoundary (topology)CurvatureDiffusionMathematical analysisReaction–diffusion systemDiffusion equationGeometryPhysicsEconomicsService (business)ThermodynamicsPhilosophyEpistemologyEconomyAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential EquationsStability and Controllability of Differential Equations