Existence and maximal Lp-regularity of solutions for the porous medium equation on manifolds with conical singularities

被引：28

作者：

Roidos, Nikolaos ^{[1
]}

Schrohe, Elmar ^{[1
]}

机构：

[1] Leibniz Univ Hannover, Inst Anal, Welfengarten 1, D-30167 Hannover, Germany

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2016年 / 41卷 / 09期

关键词：

Conically degenerate operators; fast diffusion equation; Fuchs type operators; manifolds with conical singularities; maximal L-p-regularity; porous medium equation; FOURIER MULTIPLIER THEOREMS; BOUNDED IMAGINARY POWERS; PARABOLIC EQUATIONS; DIFFERENTIAL-OPERATORS; CLOSEDNESS; SUM;

D O I：

10.1080/03605302.2016.1219745

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the porous medium equation on manifolds with conical singularities and show existence, uniqueness, and maximal L-p-regularity of a short-time solution. In particular, we obtain information on the short time asymptotics of the solution near the conical point. Our method is based on bounded imaginary powers results for cone differential operators on Mellin-Sobolev spaces and R-sectoriality perturbation techniques.

引用

页码：1441 / 1471

页数：31

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