Global Gradient Estimates for a General Type of Nonlinear Parabolic Equations

被引：4

作者：

Cavaterra, Cecilia ^{[1
,4
]}

Dipierro, Serena ^{[2
]}

Gao, Zu ^{[3
]}

Valdinoci, Enrico ^{[2
]}

机构：

[1] Univ Milan, Dipartimento Matemat Federigo Enr, Via Saldini 50, I-20133 Milan, Italy

[2] Univ Western Australia, Dept Math & Stat, 35 Stirling Highway, Crawley, WA 6009, Australia

[3] Wuhan Univ Technol, Sch Sci, Dept Math, 122 Luoshi Rd, Wuhan 430070, Hubei, Peoples R China

[4] CNR, Ist Matemat Applicata & Tecnol Informat Enrico Ma, Via Ferrata 1, I-27100 Pavia, Italy

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2022年 / 32卷 / 02期

基金：

澳大利亚研究理事会; 中央高校基本科研业务费专项资金资助;

关键词：

Parabolic equations on Riemannian manifolds; Maximum Principle; Global gradient estimates; SOUPLET-ZHANG TYPE; LIOUVILLE THEOREM; HEAT-EQUATION; ELLIPTIC-EQUATIONS; DEGENERATE; MANIFOLDS; BOUNDS;

D O I：

10.1007/s12220-021-00812-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the validity of the estimates in the global domain, and it detects several additional regularity effects due to special parabolic data. Moreover, our result comprises a large number of nonlinear sources treated by a unified approach, and it recovers many classical results as special cases.

引用

页数：37

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