Related papers: Sharp solvability for singular SDEs

It is known that spheres have negative type, but only subsets with at most one pair of antipodal points have strict negative type. These are conditions on the (angular) distances within any finite subset of points. We show that subsets with…

We show novel types of uniqueness and rigidity results for Schr\"odinger equations in either the nonlinear case or in the presence of a complex-valued potential. As our main result we obtain that the trivial solution $u=0$ is the only…

We establish some interior regularity criterions of suitable weak solutions for the 3-D Navier-Stokes equations, which allow the vertical part of the velocity to be large under the local scaling invariant norm. As an application, we improve…

In this paper we study strong approximation of the solution of a scalar stochastic differential equation (SDE) at the final time in the case when the drift coefficient may have discontinuities in space. Recently it has been shown in…

In this paper, we discuss the solvability of a p-k-Hessian entire inequality. We prove that the inequality with sub-lower-critical exponent admits no negative solutions. Moreover, the exponent is sharp. The proof is based on choosing…

This paper provides a detailed analysis of the Dirichlet boundary value problem for linear elliptic equations in divergence form with $L^p$-general drifts, where $p \in (d, \infty)$, and non-negative $L^1$-zero-order terms. Specifically, by…

We construct a family of velocity fields demonstrating the sharpness of the classical Zvonkin--Veretennikov--Davie strong well-posedness by noise regime. We consider stochastic differential equations driven by Brownian noise with drift $u$…

We provide a framework for studying the expansion rate of the image of a bounded set under a flow in Euclidean space and apply it to stochastic differential equations (SDEs for short) with singular coefficients. If the singular drift of the…

We consider stochastic evolution equations in Hilbert spaces with merely measurable and locally bounded drift term $B$ and cylindrical Wiener noise. We prove pathwise (hence strong) uniqueness in the class of global solutions. This paper…

We prove a new inequality which improves on the classical Hardy inequality in the sense that a nonlinear integral quantity with super-quadratic growth, which is computed with respect to an inverse square weight, is controlled by the energy.…

The purpose of this paper is to study the existence and uniqueness of solutions to a system of Stochastic Differential Equations (SDEs). The coordinates are bounded by zero and one, and repulse each other according to a Coulombian like…

In this article, we are interested in the strong well-posedness together with the numerical approximation of some one-dimensional stochastic differential equations with a non-linear drift, in the sense of McKean-Vlasov, driven by a…

We consider a variant of Bessel SDE by allowing the solution to be complex valued. Such SDEs appear naturally while studying the trace of Schramm-Loewner-Evolutions (SLE). We establish the existence and uniqueness of the strong solution to…

We prove strong existence and uniqueness of solutions of It\^o's stochastic time dependent equations with irregular diffusion and drift terms of Morrey class type. In a sense we are treating a "supercritical" case.

Building on results developed in https://doi.org/10.48550/arXiv.2404.14902, where It\^{o}-SDEs with possibly degenerate and discontinuous dispersion coefficient and measurable drift were analyzed with respect to a given (sub-)invariant…

In the framework of the nonsmooth critical point theory for lower semi-continuous functionals, we propose a direct variational approach to investigate the existence of infinitely many weak solutions for a class of semi-linear elliptic…

In this paper, we first establish well-posedness results for one-dimensional McKean-Vlasov stochastic differential equations (SDEs) and related particle systems with a measure-dependent drift coefficient that is discontinuous in the spatial…

We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove…

We study the singular series associated to a cubic form with integer coefficients. If the number of variables is at least $10$, we prove the absolute convergence (and hence positivity) under the assumption of Davenport's Geometric…

We study a large class of McKean-Vlasov SDEs with drift and diffusion coefficient depending on the density of the solution's time marginal laws in a Nemytskii-type of way. A McKean-Vlasov SDE of this kind arises from the study of the…