A linear proof of Hölder regularity for degenerate quasilinear parabolic equations.

Sukjung Hwang, Yonsei University, South Korea.

Speaker	Sukjung Hwang, Yonsei University, South Korea.
When	Feb 18, 2020 from 04:00 PM to 05:00 PM
Where	LH 006
Contact Name	Dr. Karthik Adimurthi
Add event to calendar	vCal iCal

Abstract: In this talk, we discuss a new proof of the Hölder regularity for weak solutions of degenerate quasilinear parabolic equations of the form

\[ u_t - \text{div} \mathcal{A}(x,t,\nabla u) = 0,\]

where the nonlinearity A( $u_{t} - div A (x, t, \nabla u) = 0,$ ) is modelled after the p-Laplace operator with (p ≥ 2) .

First, I introduce the old proof (originated by DiBenedetto in 1986) of using the intrinsic scaling, expansion of positivities, and DeGiorgi iteration. Following this, I will talk about the new proof (with K.Adimurthi) in which we develop a new intrinsic geometry based on fixing $u_{t} - div A (x, t, \nabla u) = 0,$ , which heuristically transforms the problem into studying a linear equation of the form $u_{t} - div A (x, t, \nabla u) = 0,$ _t- ∆ $u_{t} - div A (x, t, \nabla u) = 0,$ =0 . As a consequence, our estimates require just one alternative and does not use any Logarithmic estimates.