Shuntaro Tsubouchi: Continuity of spatial derivatives for parabolic (1,p) -Laplace equations

Speaker
Shuntaro Tsubouchi, University of Tokyo

AbstractWe consider a weak solution to a parabolic \((1,p)\)-Laplace equation, a singular parabolic equation that involves both the one-Laplacian and the \(p\)-Laplacian with \( 1 < p < \infty \). This talk aims to report recent developments on the continuity of spatial derivatives. Although this equation becomes no longer uniformly parabolic as a spatial gradient vanishes, the gradient continuity is proved qualitatively. This parabolic regularity result, as well as the elliptic one, is highly inspired by recent regularity studies for very degenerate problems.