caa a22 4500 445842342 CHVBK 20180317145348.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00245-010-9116-7 doi (NATIONALLICENCE)springer-10.1007/s00245-010-9116-7 Mennucci Andrea Scuola Normale Superiore Piazza dei Cavalieri 7, 56126, Pisa, Italy aut Regularity and Variationality of Solutions toHamilton—Jacobi Equations. PartII:Variationality,Existence, Uniqueness [Elektronische Daten] [Andrea Mennucci] 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 $\{p:H(x,p)\le 0\}\subset T^{*}_{x}M$, 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. Springer Science+Business Media, LLC, 2010 Hamilton-Jacobi equation nationallicence Differentiable manifold nationallicence Viscosity solution nationallicence Kuratowski convergence nationallicence Asymmetric metric space nationallicence Finsler metric nationallicence Hopf-Rinow theorem nationallicence Backward completeness nationallicence Uniqueness of solution nationallicence Applied Mathematics & Optimization Springer-Verlag 63/2(2011-04-01), 191-216 0095-4616 63:2<191 2011 63 245 https://doi.org/10.1007/s00245-010-9116-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00245-010-9116-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Mennucci Andrea Scuola Normale Superiore Piazza dei Cavalieri 7, 56126, Pisa, Italy aut NATIONALLICENCE 773 0- Applied Mathematics & Optimization Springer-Verlag 63/2(2011-04-01), 191-216 0095-4616 63:2<191 2011 63 245 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer