GRADIENT WALKS AND p-HARMONIC FUNCTIONS

被引：3

作者：

Luiro, Hannes ^{[1
]}

Parviainen, Mikko ^{[1
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, POB 35 MaD, FI-40014 Jyvaskyla, Finland

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 145卷 / 10期

基金：

芬兰科学院;

关键词：

Markov chain; stochastic representations for p-harmonic functions; tug-of-war with noise; TUG-OF-WAR; VISCOSITY SOLUTIONS; ELLIPTIC-EQUATIONS; WEAK SOLUTIONS; REGULARITY; EQUIVALENCE; LAPLACIAN;

D O I：

10.1090/proc/13540

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a class of stochastic processes having a connection to p-harmonic functions. In particular, we obtain stochastic approximations that converge uniformly to a p-harmonic function, and also with an explicit convergence rate. The main difficulty is how to deal with the zero set of the gradient of the underlying function.

引用

页码：4313 / 4324

页数：12

共 17 条

[1]

Bojarski B., 1987, BANACH CTR PUBL, V19, P25

[2] C1+ALPHA LOCAL REGULARITY OF WEAK SOLUTIONS OF DEGENERATE ELLIPTIC-EQUATIONS [J].

DIBENEDETTO, E .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1983, 7 (08) :827-850

[3]

EVANS LC, 1982, COMMUN PUR APPL MATH, V35, P334

[4]

Gilbarg D., 1983, CLASSICS MATH, DOI DOI 10.1007/978-3-642-61798-0

[5] A New Proof for the Equivalence of Weak and Viscosity Solutions for the p-Laplace Equation [J].

Julin, Vesa ;

Juutinen, Petri .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2012, 37 (05) :934-946

[6] On the equivalence of viscosity solutions and weak solutions or a quasi-linear equation [J].

Juutinen, P ;

Lindqvist, P ;

Manfredi, JJ .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2001, 33 (03) :699-717

[7] Solutions of nonlinear PDEs in the sense of averages [J].

Kawohl, Bernd ;

Manfredi, Juan ;

Parviainen, Mikko .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2012, 97 (02) :173-188

[8]

Luiro H, 2014, DIFFER INTEGRAL EQU, V27, P201

[9] Harnack's Inequality for p-Harmonic Functions via Stochastic Games [J].

Luiro, Hannes ;

Parviainen, Mikko ;

Saksman, Eero .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2013, 38 (11) :1985-2003

[10]

Manfredi JJ, 2012, ANN SCUOLA NORM-SCI, V11, P215

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