5 papers
Path-dependent Hamilton--Jacobi equations: Uniqueness results for viscosity solutions defined via families of compact sets
Mikhail I. Gomoyunov
We consider a path-dependent Hamilton--Jacobi equation with coinvariant derivatives over the space of continuous functions. We prove two uniqueness results for viscosity (generaliz…
Minimax solutions of path-dependent Hamilton--Jacobi equations under weakened assumptions with application to differential games
Mikhail Gomoyunov
We study minimax (generalized) solutions of a Cauchy problem for a (first-order) path-dependent Hamilton--Jacobi equation with co-invariant derivatives under a right-end boundary c…
Viscosity and minimax solutions for path-dependent Hamilton-Jacobi equations in infinite dimensions and related differential games
Erhan Bayraktar, Mikhail Gomoyunov, Christian Keller
We establish new results for path-dependent Hamilton-Jacobi equations with nonlinear monotone, and coercive operators on Hilbert space, which were initially studied in Bayraktar an…
Lipschitz Continuity Results for Minimax Solutions of Path-Dependent Hamilton--Jacobi Equations
Mikhail I. Gomoyunov
We consider a Cauchy problem for a (first-order) path-dependent Hamilton--Jacobi equation with coinvariant derivatives and a right-end boundary condition. Such problems arise natur…
Zero-Sum Games for Volterra Integral Equations and Viscosity Solutions of Path-Dependent Hamilton-Jacobi Equations
Mikhail I. Gomoyunov
We consider a game, in which the dynamics is described by a non-linear Volterra integral equation of Hammerstein type with a weakly-singular kernel and the goals of the first and s…