GLOBAL RESULTS FOR EIKONAL HAMILTON-JACOBI EQUATIONS ON NETWORKS

被引：7

作者：

Siconolfi, Antonio ^{[1
]}

Sorrentino, Alfonso ^{[2
]}

机构：

[1] Sapienza Univ Roma, Dept Math, Rome, Italy

[2] Univ Roma Tor Vergata, Dept Math, Rome, Italy

来源：

ANALYSIS & PDE | 2018年 / 11卷 / 01期

关键词：

Hamilton-Jacobi equation; embedded networks; graphs; viscosity solutions; viscosity subsolutions; comparison principle; discrete functional equation on graphs; Hopf-Lax formula; discrete weak KAM theory; VISCOSITY SOLUTION; BELLMAN APPROACH; MATHER THEORY; R-N; MANIFOLDS;

D O I：

10.2140/apde.2018.11.171

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a one-parameter family of eikonal Hamilton-Jacobi equations on an embedded network, and prove that there exists a unique critical value for which the corresponding equation admits global solutions, in a suitable viscosity sense. Such a solution is identified, via a Hopf-Lax-type formula, once an admissible trace is assigned on an intrinsic boundary. The salient point of our method is to associate to the network an abstract graph, encoding all of the information on the complexity of the network, and to relate the differential equation to a discrete functional equation on the graph. Comparison principles and representation formulae are proven in the supercritical case as well.

引用

页码：171 / 211

页数：41

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