Semi-concave singularities and the Hamilton-Jacobi equation

被引：0

作者：

Patrick Bernard

机构：

[1] Université Paris-Dauphine — CEREMADE (UMR 7534),

[2] École normale supérieure — Paris,undefined

来源：

Regular and Chaotic Dynamics | 2013年 / 18卷

关键词：

Hamilton-Jacobi equations; viscosity solutions; variational solutions; calculus of variations; 49L25; 37J05;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study the Cauchy problem for the Hamilton-Jacobi equation with a semiconcave initial condition. We prove an inequality between two types of weak solutions emanating from such an initial condition (the variational and the viscosity solution).We also give conditions for an explicit semi-concave function to be a viscosity solution. These conditions generalize the entropy inequality characterizing piecewise smooth solutions of scalar conservation laws in dimension one.

引用

页码：674 / 685

页数：11

共 9 条

[1]

Bernard P(2012)The Lax — Oleinik Semi-Group: A Hamiltonian Point of View Proc. Roy. Soc. Edinburgh Sect. A 192 1131-1177

[2]

Bernard P(2007)Existence of Ann. Sci. École Norm. Sup. (4) 40 445-452

[3]

Bernardi O(2011) Critical Sub-Solutions of the Hamilton — Jacobi Equation on Compact Manifolds Discrete Contin. Dyn. Syst. 31 385-406

[4]

Cardin F(2001)On J. Nonlinear Convex Anal. 2 333-343

[5]

Imbert C(1986)-Variational Solutions for Hamilton — Jacobi Equations Proc. Amer. Math. Soc. 96 79-84

[6]

Lions P-L(2006)Convex Analysis Techniques for Hopf — Lax Formulae in Hamilton — Jacobi Equations ESAIM Control Optim. Calc. Var. 12 795-815

[7]

Rochet J-C(1992)Hopf Formula and Multitime Hamilton — Jacobi Equations Math. Ann. 292 685-710

[8]

McCaffey D(undefined)Graph Selectors and Viscosity Solutions on LagrangianManifolds undefined undefined undefined-undefined

[9]

Viterbo C(undefined)Symplectic Topology as the Geometry of Generating Functions undefined undefined undefined-undefined

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