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On global discontinuous solutions of Hamilton-Jacobi equations

Abstract:

The uniqueness of classical semicontinuous viscosity solutions of the Cauchy problem for Hamlton-Jacobi equations is established for globally Lipschitz continuous and convex Hamiltonian H = H(Du), provided the discontinuous initial value function (x) is continuous outside a set Γ of measure zero and satisfies A formula is presented. We prove that the discontinuous solutions with almost everywhere continuous initial data satisfying (*) become Lipschitz continuous after finite time for locally ...

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Journal:
Comptes Rendus Mathematique
Volume:
334
Issue:
2
Pages:
113-118
Publication date:
2002-01-30
DOI:
ISSN:
1631-073X
URN:
uuid:1b48278e-b966-4cbd-af6e-b8e3a2a888a9
Source identifiers:
203141
Local pid:
pubs:203141
Language:
English

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