On the differentiability of the solutions of non-local Isaacs equations\n involving frac 12-Laplacian

2014/12/15 by Imran H. Biswas, Indranil Chowdhury, Biswas, Imran H +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1412.4756

openalex publication_date 2014/12/15 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28

Abstract

We derive C^1,\σ-estimate for the solutions of a class of non-local\nelliptic Bellman-Isaacs equations. These equations are fully nonlinear and are\nassociated with infinite horizon stochastic differential game problems\ninvolving jump-diffusions. The non-locality is represented by the presence of\nfractional order diffusion term and we deal with the particular case of frac\n12-Laplacian, where the order frac 12 is known as the critical order in\nthis context. More importantly, these equations are not translation invariant\nand we prove that the viscosity solutions of such equations are C^1,\σ,\nmaking the equations classically solvable.\n

Citations

• The Evans-Krylov theorem for nonlocal fully nonlinear equations

Related

• On the rate of convergence for monotone numerical schemes for nonlocal\n Isaacs' equations
• To the theory of viscosity solutions for uniformly elliptic Isaacs equations
• To the theory of viscosity solutions for uniformly parabolic Isaacs equations
• On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusion
• On representation and regularity of viscosity solutions to degenerate Isaacs equations and certain nonconvex Hessian equations