ENERGY ESTIMATES FOR VARIATIONAL MINIMIZERS OF A PARABOLIC DOUBLY NONLINEAR EQUATION ON METRIC MEASURE SPACES

被引：6

作者：

Ivert, Per-Anders

Marola, Niko ^{[1
]}

Masson, Mathias ^{[2
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, FI-00014 Helsinki, Finland

[2] Aalto Univ, Sch Sci & Technol, Dept Math, FI-00076 Aalto, Finland

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2014年 / 39卷 / 02期

关键词：

Doubling measure; energy estimates; Harnack inequality; parabolic minimizer; Poincare inequality; subminimizer; superminimizer; INEQUALITY;

D O I：

10.5186/aasfm.2014.3936

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper a variational approach is taken to study a doubly nonlinear parabolic equation. We consider energy estimates for parabolic minimizers related to this equation. These energy estimates play a fundamental role in obtaining Harnack estimates. Our treatment is done in general metric measure spaces with a doubling measure and a Poincare inequality.

引用

页码：711 / 719

页数：9

共 50 条

[1] Gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces
Yang, Fei
Zhang, Liangdi
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 187 : 49 - 70
[2] Gradient Estimates for a Nonlinear Parabolic Equation on Complete Smooth Metric Measure Spaces
Zeng, Fanqi
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2021, 18 (04)
[3] Gradient Estimates for a Nonlinear Parabolic Equation on Complete Smooth Metric Measure Spaces
Fanqi Zeng
Mediterranean Journal of Mathematics, 2021, 18
[4] Existence of parabolic minimizers on metric measure spaces
Collins, Michael
Heran, Andreas
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2018, 176 : 56 - 83
[5] Gradient estimates and Harnack inequalities for a nonlinear parabolic equation on smooth metric measure spaces
Yang, Fei
Zhang, Liangdi
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 268 (08) : 4577 - 4617
[6] Li-yau estimates for a nonlinear parabolic equation on Finsler metric measure spaces
Shen, Bin
Zhu, Yuhan
MANUSCRIPTA MATHEMATICA, 2025, 176 (02)
[7] Stability for parabolic quasi minimizers in metric measure spaces
Fujishima, Yohei
Habermann, Jens
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, 2018, 29 (02) : 343 - 376
[8] ON THE HARNACK INEQUALITY FOR PARABOLIC MINIMIZERS IN METRIC MEASURE SPACES
Marola, Niko
Masson, Mathias
TOHOKU MATHEMATICAL JOURNAL, 2013, 65 (04) : 569 - 589
[9] Gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces with evolving metrics and potentials
Taheri, Ali
Vahidifar, Vahideh
NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2023, 232
[10] Existence of parabolic minimizers to the total variation flow on metric measure spaces
Buffa, Vito
Collins, Michael
Camacho, Cintia Pacchiano
MANUSCRIPTA MATHEMATICA, 2023, 170 (1-2) : 109 - 145

← 1 2 3 4 5 →