Hamilton-Jacobi in metric spaces with a homological term
| Autor: | Ugo Bessi |
|---|---|
| Přispěvatelé: | Bessi, Ugo |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Applied Mathematics 010102 general mathematics Mathematics::Optimization and Control 01 natural sciences Hamilton–Jacobi equation Term (time) 010101 applied mathematics Metric space Hamilton-Jacobi theory metric measure spaces Curvature bounded from below Mathematics - Analysis of PDEs Optimization and Control (math.OC) FOS: Mathematics 0101 mathematics Value (mathematics) Mathematics - Optimization and Control Analysis Analysis of PDEs (math.AP) Mathematics |
| Popis: | The Hamilton-Jacobi equation on metric spaces has been studied by several authors; following the approach of Gangbo and Swiech, we show that the final value problem for the Hamilton-Jacobi equation has a unique solution even if we add a homological term to the Hamiltonian. In metric measure spaces which satisfy the $RCD(K,\infty)$ condition one can define a Laplacian which shares many properties with the ordinary Laplacian on $\R^n$; in particular, it is possible to formulate a viscous Hamilton-Jacobi equation. We show that, if the homological term is sufficiently regular, the viscous Hamilton-Jacobi equation has a unique solution also in this case. |
| Databáze: | OpenAIRE |
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