Hölder continuity for a doubly nonlinear equation

Abstract: The prototype of the partial differential equations considered in this talk is $$ \partial_t \big( |u|^{q-1} u \big) - \operatorname{div} \big( |Du|^{p-2} Du \big) = 0 \quad \text{in } E_T = E \times (0,T] \subset \mathbb{R}^{N+1} $$ with parameters $q>0$ and $p>1$. Well-known special cases of this doubly nonlinear equation are the porous medium equation ($p=2$), the parabolic $p$-Laplace equation ($q=1$) and Trudinger's equation ($q=p-1$). I will present H\"older continuity results based on joint work with Verena B\"ogelein, Frank Duzaar and Naian Liao.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

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