On the regularizing effect for unbounded solutions of first-order Hamilton-Jacobi equations
نویسندگان
چکیده
We give a simplified proof of regularizing effects for first-order Hamilton-Jacobi Equations of the form ut+H(x, t, Du) = 0 in R ×(0,+∞) in the case where the idea is to first estimate ut. As a consequence, we have a Lipschitz regularity in space and time for coercive Hamiltonians and, for hypo-elliptic Hamiltonians, we also have an Hölder regularizing effect in space following a result of L. C. Evans and M. R. James.
منابع مشابه
De Giorgi Techniques Applied to Hamilton-jacobi Equations with Unbounded Right-hand Side
In this article we obtain Hölder estimates for solutions to second-order Hamilton-Jacobi equations with super-quadratic growth in the gradient and unbounded source term. The estimates are uniform with respect to the smallness of the diffusion and the smoothness of the Hamiltonian. Our work is in the spirit of a result by P. Cardaliaguet and L. Silvestre [5]. We utilize De Giorgi’s method, which...
متن کاملUniqueness for unbounded solutions to stationary viscous Hamilton–Jacobi equations
We consider a class of stationary viscous Hamilton–Jacobi equations as
متن کاملUniqueness 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 کاملA Paraxial Formulation for the Viscosity Solution of Quasi-P Eikonal Equations
Stationary quasi-P eikonal equations, stationary Hamilton-Jacobi equations, arise from the asymptotic approximation of anisotropic wave propagation. A paraxial formulation of the quasi-P eikonal equation results in a paraxial quasi-P eikonal equation, an evolution Hamilton-Jacobi equation in a preferred direction, which provides a fast and efficient way for computing viscosity solutions of quas...
متن کامل