Journal of the Korean Mathematical Society (대한수학회지)
- Volume 33 Issue 1
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- Pages.31-38
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- 1996
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
A STABILITY RESULT FOR DIRICHLET PROBLEM OF THE FIRST-ORDER HAMILTON-JACOBI EQUATIONS
Abstract
It is well known that Dirichlet problem of the first-order Hamilton-Jacobi equations $$ (H-J) u(x) + H(\nabla u(x)) = f(x), x \in R^N, $$ does not have a classical solution even though the Hamiltonian H is smooth.