Regularity and Variationality of Solutions to Hamilton-Jacobi Equations. Part II: Variationality, Existence, Uniqueness
Journal Article
·
· Applied Mathematics and Optimization
- Scuola Normale Superiore Piazza dei Cavalieri 7 (Italy)
We formulate an Hamilton-Jacobi partial differential equation H(x, Du(x))=0 on a n dimensional manifold M, with assumptions of convexity of the sets {l_brace}p:H(x,p){<=}0) is a subset of T{sub x}*M, for all x.We reduce the above problem to a simpler problem; this shows that u may be built using an asymmetric distance (this is a generalization of the 'distance function' in Finsler geometry); this brings forth a 'completeness' condition, and a Hopf-Rinow theorem adapted to Hamilton-Jacobi problems. The 'completeness' condition implies that u is the unique viscosity solution to the above problem.
- OSTI ID:
- 22043935
- Journal Information:
- Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 2 Vol. 63; ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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