2018/01/30 by Valentine Roos, Roos, Valentine
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Stochastic processes and financial applications #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1801.09889
openalex publication_date 2018/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Cauchy problem for the first order evolutive Hamilton-Jacobi equation with a Lipschitz initial condition. The Hamiltonian is not necessarily convex in the momentum variable and not a priori compactly supported. We build and study an operator giving a variational solution of this problem, and get local Lipschitz estimates on this operator. Iterating this variational operator we obtain the viscosity operator and extend the estimates to the viscosity framework. We also check that the construction of the variational operator gives the Lax-Oleinik semigroup if the Hamiltonian is convex or concave in the momentum variable.