Hölder Regularity for Viscosity Solutions of Fully Nonlinear, Local or Nonlocal, Hamilton-Jacobi Equations with Superquadratic Growth in the Gradient
نویسندگان
چکیده
Viscosity solutions of fully nonlinear, local or non local, Hamilton-Jacobi equations with a super-quadratic growth in the gradient variable are proved to be Hölder continuous, with a modulus depending only on the growth of the Hamiltonian. The proof involves some representation formula for nonlocal Hamilton-Jacobi equations in terms of controlled jump processes and a weak reverse inequality.
منابع مشابه
A Short Proof of the C–regularity of Viscosity Subsolutions for Superquadratic Viscous Hamilton-jacobi Equations and Applications
Recently I. Capuzzo Dolcetta, F. Leoni and A. Porretta obtain a very surprising regularity result for fully nonlinear, superquadratic, elliptic equations by showing that viscosity subsolutions of such equations are locally Hölder continuous, and even globally if the boundary of the domain is regular enough. The aim of this paper is to provide a simplified proof of their results, together with a...
متن کاملHölder estimates in space - time for viscosity solutions of Hamilton - Jacobi equations ∗
It is well-known that solutions to the basic problem in the calculus of variations may fail to be Lipschitz continuous when the Lagrangian depends on t. Similarly, for viscosity solutions to time-dependent Hamilton-Jacobi equations one cannot expect Lipschitz bounds to hold uniformly with respect to the regularity of coefficients. This phenomenon raises the question whether such solutions satis...
متن کاملSolvability of uniformly elliptic fully nonlinear PDE
We get existence, uniqueness and non-uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of Hamilton-Jacobi-BellmanIsaacs type, with unbounded ingredients and quadratic growth in the gradient, without hypotheses of convexity or properness. Some of our results are new even for equations in divergence form.
متن کاملA note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable
for some δ > 0. Regularity of solutions of Hamilton-Jacobi equations with superlinear growth have been the object of several works (see in particular Lions [6], Barles [3], Rampazzo, Sartori [7]). Our aim is to show that u is locally Hölder continuous with Hölder exponent and constant depending only M , δ, q and T . What is new compared to the previous works is that the regularity does not depe...
متن کاملPerron’s method for nonlocal fully nonlinear equations
This paper is concerned with existence of viscosity solutions of non-translation invariant nonlocal fully nonlinear equations. We construct a discontinuous viscosity solution of such nonlocal equation by Perron’s method. If the equation is uniformly elliptic, we prove the discontinuous viscosity solution is Hölder continuous and thus it is a viscosity solution.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Control and Optimization
دوره 49 شماره
صفحات -
تاریخ انتشار 2011