Error Estimates for Viscosity Solutions of Hamilton{Jacobi Equation under Quadratic Growth Conditions
نویسنده
چکیده
In this paper we develop a comparison lemma for viscosity solutions for the Hamilton{ Jacobi equations. We consider locally Lipschitz solutions with quadratic growth and assume the quadratic growth of the Hamiltonian. An error estimate of viscosity solutions using the weighted sup norm is obtained.
منابع مشابه
Uniqueness results for convex Hamilton - Jacobi equations under p > 1 growth conditions on data
Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness of viscosity solutions growing at most like o(1+ |x|p) at infinity for such HJB equations and more generally for degenerate parabolic equations with a superli...
متن کامل[hal-00327496, v1] Uniqueness results for convex Hamilton-Jacobi equations under $p>1$ growth conditions on data
Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness of viscosity solutions growing at most like o(1+ |x|p) at infinity for such HJB equations and more generally for degenerate parabolic equations with a superli...
متن کاملOptimal Control of Nonlinear Uncertain Systems over an Infinite Horizon via Finite-Horizon Approximations
It is well-known that the Hamilton-Jacobi-Isaacs (HJI) equation associated with a nonlinear H-optimal control problem on an infinite-time horizon generally admits nonunique, and in fact infinitely many, viscosity solutions. This makes it difficult to pick the relevant viscosity solution for the problem at hand, particularly when it is computed numerically. For the finitehorizon version of the p...
متن کاملOn viscosity solutions of certain Hamilton-Jacobi equations: Regularity results and generalized Sard's Theorems
Under usual assumptions on the Hamiltonian, we prove that any viscosity solution of the corresponding Hamilton-Jacobi equation on the manifold M is locally semiconcave and C loc outside the closure of its singular set (which is nowhere dense in M). Moreover, we prove that, under additional assumptions and in low dimension, any viscosity solution of that Hamilton-Jacobi equation satisfies a gene...
متن کاملUniqueness of Constrained Viscosity Solutions in Hybrid Control Systems
We study constrained viscosity solutions with an unbounded growth for a class of first order Hamilton–Jacobi–Bellman equations arising in hybrid control systems. To deal with the boundary constraint and rapid growth of the solutions, we construct a particular set of test functions and under very mild conditions establish a comparison theorem which gives the estimate of distance between the subs...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009