Hölder Estimates for Nonlocal-diffusion Equations with Drifts

Hölder regularity for generalized master equations with rough kernels

We prove Hölder estimates for integro-differential equations related to some continuous time random walks. These equations are nonlocal both in space and time and recover classical parabolic equations in limit cases. For some values of the parameters, the equations exhibit at the same time finite speed of propagation and C regularization.

Continuous Dependence Estimates for Nonlinear Fractional Convection-diffusion Equations

We develop a general framework for finding error estimates for convection-diffusion equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators that are generators of pure jump Lévy processes (e.g. the fractional Laplacian). As an application, we derive continuous dependence estimates on the nonlinea...

The Generalized Diffusion Phenomenon and Applications

We study the asymptotic behavior of solutions to dissipative wave equations involving two non-commuting self-adjoint operators in a Hilbert space. The main result is that the abstract diffusion phenomenon takes place, as solutions of such equations approach solutions of diffusion equations at large times. When the diffusion semigroup has the Markov property and satisfies a Nash-type inequality,...

Hölder Estimates and Large Time Behavior for a Nonlocal Doubly Nonlinear Evolution

Error estimates for finite difference-quadrature schemes for a class of nonlocal Bellman equations with variable diffusion

We derive error estimates for certain approximate solutions of Bellman equations associated to a class of controlled jump-diffusion (Lévy) processes. These Bellman equations are fully nonlinear degenerate integroPDEs interpreted in the sense of viscosity solutions. The approximate solutions are generated by an implicit finite difference-quadrature scheme.