偏微分方程式セミナー: A lower spatially Lipschitz bound for solutions to fully nonlinear parabolic equations and its optimality, 浜向 直 氏

Time：16:30-17:30

Place：online

Organizer：黒田 紘敏、浜向 直、古屋 貴士

Speaker：浜向 直 氏 (北海道大学)

Title：A lower spatially Lipschitz bound for solutions to fully nonlinear parabolic equations and its optimality

Abstract：We derive a lower spatially Lipschitz bound for viscosity solutions to fully nonlinear parabolic partial differential equations when the initial datum is singular but belongs to the Hölder space. Our estimate gives the optimal rate of Lipschitz regularizing effects for solutions, which occur for some uniformly parabolic equations and first order Hamilton-Jacobi equations.

This talk is based on a joint work with Suguru Kikkawa (Fujitsu Japan Limited).