On a class of first order Hamilton–Jacobi equations in metric spaces

By Luigi Ambrosio, Jin Feng. 2014

87 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5772ac2fcf6068a8fe43d6cb08baba7609eec881

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Existence of a solution to an equation arising from the theory of Mean Field Games (2015, methodology): “The starting point of our work is the value function U which is the unique metric viscosity solution, in the sense of [19] and [20] (see also [2] and [18]), to the Hamilton– Jacobi equation (1.”
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”
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.”
The Master Equation and the Convergence Problem in Mean Field Games (2015, background): “It is worth mentioning that the master equation (9) is not the first example of an equation studied in the space of measures –by far: for instance Otto [58] gave an interpretation of the porous medium equation as an evolution equation in the space of measures, and Jordan, Kinderlehrer and Otto [38] ”
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]).”