Metric viscosity solutions of Hamilton–Jacobi equations depending on local slopes

By Wilfrid Gangbo, Andrzej Swiech. 2015

59 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/05afdd57ada471345ec0d778310d780ad03d455e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Luca Tamanini
2. Cong Wu
3. Jianfeng Zhang
4. Huyen Pham
5. Wilfrid Gangbo
6. Andrea Cosso
7. Idris Kharroubi
8. Mauro Rosestolato

In Geometry and Topology

1. Jianfeng Zhang
2. Luca Tamanini
3. Cong Wu
4. Huyen Pham
5. Andrea Cosso
6. Wilfrid Gangbo
7. Mauro Rosestolato
8. Fausto Gozzi

Citations in the corpus

• Bellman equation and viscosity solutions for mean-field stochastic control problem (2015, unknown): “There are several definitions of viscosity solutions for Hamilton Jacobi equations of first order in Wasserstein space and more generally in metric spaces, see e.g. [2, 19, 22] or [23].”
• Second order differentiation formula on RCD*$(K,N)$ spaces (2018, methodology): “In this direction, it is worth recalling that in [2] and [21] it has been developed a theory of viscosity solutions for some first-order Hamilton-Jacobi equations on metric spaces.”
• Viscosity solutions to parabolic master equations and McKean–Vlasov SDEs with closed-loop controls (2018, background): “There are several works for first order master equations corresponding to the deterministic setting, see e.g. Cardaliaguet [7], Gangbo & Swiech [21, 22], and Bensoussan & Yam [4].”
• On differentiability in the Wasserstein space and well-posedness for Hamilton–Jacobi equations (2019, background): “Other works [1], [16] on Hamilton-Jacobi equations in the Wasserstein space deal with more general metric settings and have various degrees of generality (either special types of Hamiltonians depending on metric derivatives and/or concepts of viscosity solutions based on special types of test functi”
• Master Bellman equation in the Wasserstein space: Uniqueness of viscosity solutions (2021, background): “There are already wellposedness results in the first-order case, see [2, 25, 1, 26, 27, 28], even for equations adopting different notions of derivative with respect to the measure.”
• Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks (2013, background): “Recently, a general approach of eikonal equations in metric spaces has been proposed in [28, 5, 24] (see also [36]).”