### On representation formulas for Hamilton Jacobi's equations related to calculus of variations problems

DOI: http://dx.doi.org/10.12775/TMNA.2002.027

#### Abstract

In this paper, existence and uniqueness of generalized solutions

of some first order Hamilton Jacobi equations are proved. This

task is accomplished by showing that the value function for a

certain problem of the calculus of variations is the unique

solution of the PDE. This can be viewed as a representation

formula of the solution.

of some first order Hamilton Jacobi equations are proved. This

task is accomplished by showing that the value function for a

certain problem of the calculus of variations is the unique

solution of the PDE. This can be viewed as a representation

formula of the solution.

#### Keywords

Calculus of variations; viability theory; discontinuous viscosity solutions; uniqueness for Hamilton Jacobi's equations

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