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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