On Viscosity Solutions of Hamilton-Jacobi Equations in the Wasserstein space and the Vanishing Viscosity Limit
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917213646094336 |
|---|---|
| author | Silberstein, Giacomo Ceccherini Tonon, Daniela |
| author_facet | Silberstein, Giacomo Ceccherini Tonon, Daniela |
| contents | The aim of this article is twofold. First, we develop a unified framework for viscosity solutions to both first-order Hamilton-Jacobi equations and semilinear Hamilton-Jacobi equations driven by the idiosyncratic operator, defined on the Wasserstein Space. Second, we establish a vanishing-viscosity limit-extending beyond the classical control-theoretic setting-for solutions of semilinear Hamilton-Jacobi equations, proving their convergence to the corresponding first-order solution as the idiosyncratic noise vanishes. Our approach provides an optimal convergence rate. We also present some results of independent interest. These include existence theorems for the first-order equation, obtained through an appropriate Hopf-Lax representation, and a useful description of the action of the idiosyncratic operator on geodesically convex functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14568 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Viscosity Solutions of Hamilton-Jacobi Equations in the Wasserstein space and the Vanishing Viscosity Limit Silberstein, Giacomo Ceccherini Tonon, Daniela Analysis of PDEs Metric Geometry Optimization and Control The aim of this article is twofold. First, we develop a unified framework for viscosity solutions to both first-order Hamilton-Jacobi equations and semilinear Hamilton-Jacobi equations driven by the idiosyncratic operator, defined on the Wasserstein Space. Second, we establish a vanishing-viscosity limit-extending beyond the classical control-theoretic setting-for solutions of semilinear Hamilton-Jacobi equations, proving their convergence to the corresponding first-order solution as the idiosyncratic noise vanishes. Our approach provides an optimal convergence rate. We also present some results of independent interest. These include existence theorems for the first-order equation, obtained through an appropriate Hopf-Lax representation, and a useful description of the action of the idiosyncratic operator on geodesically convex functions. |
| title | On Viscosity Solutions of Hamilton-Jacobi Equations in the Wasserstein space and the Vanishing Viscosity Limit |
| topic | Analysis of PDEs Metric Geometry Optimization and Control |
| url | https://arxiv.org/abs/2512.14568 |