Related papers: Harnack estimates for nonlocal drift-diffusion equ…

In this paper we extend previous results on the regularity of solutions of integro-differential parabolic equations. The kernels are non necessarily symmetric which could be interpreted as a non-local drift with the same order as the…

We study a class of nonlocal-diffusion equations with drifts, and derive a priori $\Phi$-H\"older estimate for the solutions by using a purely probabilistic argument, where $\Phi$ is an intrinsic scaling function for the equation.

The purpose of this paper is to prove new fine regularity results for nonlocal drift-diffusion equations via pointwise potential estimates. Our analysis requires only minimal assumptions on the divergence free drift term, enabling us to…

This paper is concerned with nonlinear elliptic equations in nondivergence form where the operator has a first order drift term which is not Lipschitz continuous. Under this condition the equations are nonhomogeneous and nonnegative…

We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate…

This note is devoted to some nonlocal, nonlinear elliptic problems with an emphasis on the computation of the solution of such problems, reducing it in particular to a fixed point argument in R. Errors estimates and numerical experiments…

We prove a Harnack inequality for functions which, at points of large gradient, are solutions of elliptic equations with unbounded drift.

We obtain an analytic proof for asymptotic H\"older estimate and Harnack's inequality for solutions to a discrete dynamic programming equation. The results also generalize to functions satisfying Pucci-type inequalities for discrete…

The primary objective of this work is to establish pointwise gradient estimates for solutions to a class of parabolic nonlinear nonlocal measure data problems, expressed in terms of caloric Riesz potentials of the data. As a consequence of…

We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be…

We study existence and Lorentz regularity of distributional solutions to elliptic equations with either a convection or a drift first order term. The presence of such a term makes the problem not coercive. The main tools are pointwise…

We prove interior Harnack's inequalities for solutions of fractional nonlocal equations. Our examples include fractional powers of divergence form elliptic operators with potentials, operators arising in classical orthogonal expansions and…

We prove a full Harnack inequality for local minimizers, as well as weak solutions to nonlocal problems with non-standard growth. The main auxiliary results are local boundedness and a weak Harnack inequality for functions in a…

We consider nonlinear drift-diffusion equations (both porous medium equations and fast diffusion equations) with a measure-valued external force. We establish existence of nonnegative weak solutions satisfying gradient estimates, provided…

This paper considers a class of nonlinear, degenerate drift- diffusion equations. We study well-posedness and regularity properties of the solutions, with the goal to achieve uniform H\"{o}lder regularity in terms of $L^p$-bound on the…

We study weak solutions to nonlocal equations governed by integrodifferential operators. Solutions are defined with the help of symmetric nonlocal bilinear forms. Throughout this work, our main emphasis is on operators with general,…

Using a classical technique introduced by Achi E. Brandt for elliptic equations, we study a general class of nonlocal equations obtained as a superposition of classical and fractional operators in different variables. We obtain that the…

We establish new Harnack estimates that defy the waiting-time phenomenon for global solutions to nonlocal parabolic equations. Our technique allows us to consider general nonlocal operators with bounded measurable coefficients. Moreover, we…

We study the long-time dynamics of the nonlinear processes modeled by diffusion-transport partial differential equations in non-divergence form with drifts. The solutions are subject to some inhomogeneous Dirichlet boundary condition.…

A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator…