Well-posedness for a transmission problem connecting first and second-order operators

2023/05/29 by Héctor A. Chang‐Lara, Chang-Lara, Héctor A.
Economics, Econometrics and Finance · Mathematics · #35B51 #35D40 #35F21 #49L12 #49L25 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2305.18659

openalex publication_date 2023/05/29 · openalex created_date 2023/06/01 · openalex updated_date 2026/07/28

Abstract

We establish the existence and uniqueness of viscosity solutions within a domain Ω⊆\mathbb Rⁿ for a class of equations governed by elliptic and eikonal type equations in disjoint regions. Our primary motivation stems from the Hamilton-Jacobi equation that arises in the context of a stochastic optimal control problem.

Related

• Viscosity Solutions to Second Order Path-Dependent Hamilton-Jacobi-Bellman Equations in Hilbert Spaces
• Viscosity solutions for junctions: well posedness and stability
• Viscosity Solutions to First Order Path-Dependent Hamilton-Jacobi-Bellman Equations in Hilbert Space
• Viscosity Solutions to Second Order Path-Dependent Hamilton-Jacobi-Bellman Equations and Applications
• The existence and uniqueness of viscosity solution to a kind of Hamilton-Jacobi-Bellman equations