Uniqueness of Viscosity Solutions of a Geometric Fully Nonlinear Parabolic Equation
نویسندگان
چکیده
We observe that the comparison result of Barles-Biton-Ley for viscosity solutions of a class of nonlinear parabolic equations can be applied to a geometric fully nonlinear parabolic equation which arises from the graphic solutions for the Lagrangian mean curvature flow.
منابع مشابه
Introduction to fully nonlinear parabolic equations
These notes contain a short exposition of selected results about parabolic equations: Schauder estimates for linear parabolic equations with Hölder coefficients, some existence, uniqueness and regularity results for viscosity solutions of fully nonlinear parabolic equations (including degenerate ones), the Harnack inequality for fully nonlinear uniformly parabolic equations. MSC. 35K55, 35D40, ...
متن کاملViscosity Solutions of Fully Nonlinear Parabolic Path Dependent Pdes: Part Ii by Ibrahim Ekren,
In our previous paper [Ekren, Touzi and Zhang (2015)], we introduced a notion of viscosity solutions for fully nonlinear path-dependent PDEs, extending the semilinear case of Ekren et al. [Ann. Probab. 42 (2014) 204– 236], which satisfies a partial comparison result under standard Lipshitz-type assumptions. The main result of this paper provides a full, well-posedness result under an additional...
متن کاملSecond Order Hamilton--Jacobi Equations in Hilbert Spaces and Stochastic Boundary Control
The paper is concerned with fully nonlinear second order Hamilton{Jacobi{Bellman{ Isaacs equations of elliptic type in separable Hilbert spaces which have unbounded rst and second order terms. The viscosity solution approach is adapted to the equations under consideration and the existence and uniqueness of viscosity solutions is proved. A stochastic optimal control problem driven by a paraboli...
متن کاملConvergence of Rothe’s Method for Fully Nonlinear Parabolic Equations
Convergence of Rothe’s method for the fully nonlinear parabolic equation ut +F (D 2u,Du, u, x, t) = 0 is considered under some continuity assumptions on F. We show that the Rothe solutions are Lipschitz in time, and they solve the equation in the viscosity sense. As an immediate corollary we get Lipschitz behavior in time of the viscosity solutions of our equation.
متن کاملGeneral existence and uniqueness of viscosity solutions for impulse control of jump-diffusions
General theorems for existence and uniqueness of viscosity solutions for HamiltonJacobi-Bellman quasi-variational inequalities (HJBQVI) with integral term are established. Such nonlinear partial integro-differential equations (PIDE) arise in the study of combined impulse and stochastic control for jump-diffusion processes. The HJBQVI consists of an HJB part (for stochastic control) combined wit...
متن کامل