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

Sukjung Hwang, Yonsei University, South Korea.
 Speaker Sukjung Hwang, Yonsei University, South Korea. Feb 18, 2020 from 04:00 PM to 05:00 PM LH 006 Dr. Karthik Adimurthi 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(x,t,u) 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, which heuristically transforms the problem into studying a linear equation of the form ut- ∆u=0 . As a consequence, our estimates require just one alternative and does not use any Logarithmic estimates.

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