The fractional porous medium equation on noncompact Riemannian manifolds

被引：1

作者：

Berchio, Elvise ^{[1
]}

Bonforte, Matteo ^{[2
,3
]}

Grillo, Gabriele ^{[4
]}

Muratori, Matteo ^{[4
]}

机构：

[1] Politecn Torino, Dipartimento Sci Matematiche, Corso Duca Abruzzi 24, I-10129 Turin, Italy

[2] Univ Autonoma Madrid, Dept Matemat, Campus Cantoblanco, Madrid 28049, Spain

[3] UCM, Inst Ciencias Matemat ICMAT, UAM UC3M, CSIC, Campus Cantoblanco, Madrid 28049, Spain

[4] Politecn Milan, Dipartimento Matemat, Piazza Leonardo Vinci 32, I-20133 Milan, Italy

来源：

MATHEMATISCHE ANNALEN | 2024年 / 389卷 / 04期

基金：

欧盟地平线“2020”;

关键词：

DEGENERATE DIFFUSION-EQUATIONS; ASYMPTOTIC-BEHAVIOR; EXISTENCE; REGULARITY; UNIQUENESS; LAPLACIAN; KERNEL;

D O I：

10.1007/s00208-023-02731-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study nonnegative solutions to the fractional porous medium equation on a suitable class of connected, noncompact Riemannian manifolds. We provide existence and smoothing estimates for solutions, in an appropriate weak (dual) sense, for data belonging either to the usual L-1 space or to a considerably larger weighted space determined in terms of the fractional Green function. The class of manifolds for which the results hold includes both the Euclidean and the hyperbolic spaces and even in the Euclidean situation involves a class of data which is larger than the previously known one.

引用

页码：3603 / 3651

页数：49

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