相关论文: Regularity results for degenerate Kolmogorov equat…
In this article we establish regularity properties for solutions of infinite dimensional Kolmogorov equations. We prove that if the nonlinear drift coefficients, the nonlinear diffusion coefficients, and the initial conditions of the…
In this paper we prove regularity results for a class of nonlinear degenerate elliptic equations of the form $\displaystyle -\operatorname{div}(A(|\nabla u|)\nabla u)+B\left( |\nabla u|\right) =f(u)$; in particular, we investigate the…
The aim of this paper is to establish new pointwise regularity results for solutions to degenerate second order partial differential equations with a Kolmogorov-type operator of the form $$\mathscr{L} :=\sum_{i,j=1}^m \partial^2_{x_i x_j }…
We study value functions which are viscosity solutions of certain Kolmogorov equations. Using PDE techniques we prove that they are $C^{1,\alpha}$ regular on special finite dimensional subspaces. The problem has origins in pricing and…
We consider solutions to degenerate anisotropic elliptic equations in order to study their regularity. In particular we establish second-order estimates and enclose regularity results for the stress field. All our results are new even in…
We consider a class of degenerate equations satisfying a parabolic H\"ormander condition, with coefficients that are measurable in time and H\"older continuous in the space variables. By utilizing a generalized notion of strong solution, we…
Sobolev-type regularity results are proved for solutions to a class of second order elliptic equations with a singular or degenerate weight, under non-homogeneous Neumann conditions. As an application a Pohozaev-type identity for weak…
In $\mathbb R^d$, $d \geq 3$, consider the divergence and the non-divergence form operators \begin{equation} \tag{$i$} -\Delta - \nabla \cdot (a-I) \cdot \nabla + b \cdot \nabla, \end{equation} \begin{equation} \tag{$ii$} - \Delta - (a-I)…
We obtain Calder{\'o}n-Zygmund estimates for some degenerate equations of Kolmogorov type with inhomogeneous coefficients. We then derive the well-posedness of the martingale problem associated to related degenerate operators, and therefore…
We consider a possibly strongly degenerate parabolic semilinear problem which can be applied to a differential model for pricing financial derivatives. We prove the asked regularity for applying the Ito's formula which is used for building…
We consider an elliptic Kolmogorov equation $\lambda u - Ku = f$ in a separable Hilbert space $H$. The Kolmogorov operator $K$ is associated to an infinite dimensional convex gradient system: $dX = (AX - DU(X))dt + dW (t)$, where $A $ is a…
The aim of this note is to prove sharp regularity estimates for solutions of the continuity equation associated to vector fields of class $W^{1,p}$ with $p>1$. The regularity is of "logarithmic order" and is measured by means of suitable…
We prove the local boundedness of the solutions to degenerate second order partial differential equations of Kolmogorov type with measurable coefficients in divergence form, under minimal integrability assumption on the lower order…
The celebrated H\"{o}rmander condition is a sufficient (and nearly necessary) condition for a second-order linear Kolmogorov partial differential equation (PDE) with smooth coefficients to be hypoelliptic. As a consequence, the solutions of…
We provide new regularity results for the solutions of the Kolmogorov equation associated to a SPDE with nonlinear diffusion coefficients and a Burgers type nonlinearity. This generalizes previous results in the simpler cases of additive or…
We develop regularity theory for elliptic Kolmogorov operator with divergence-free drift in a large class (or, more generally, drift having singular divergence). A key step in our proofs is "Caccioppoli's iterations", used in addition to…
We study the regularity properties of the second order linear operator in $\mathbb{R}^{N+1}$: \begin{equation*} \mathscr{L} u := \sum_{j,k= 1}^{m} a_{jk}\partial_{x_j x_k}^2 u + \sum_{j,k= 1}^{N} b_{jk}x_k \partial_{x_j} u - \partial_t u,…
We investigate the iterative methods proposed by Maz'ya and Kozlov (see [KM1], [KM2]) for solving ill-posed inverse problems modeled by partial differential equations. We consider linear evolutionary problems of elliptic, hyperbolic and…
We examine nonlinear Kolmogorov partial differential equations (PDEs). Here the nonlinear part of the PDE comes from its Hamiltonian where one maximizes over all possible drift and diffusion coefficients which fall within a…
This paper is concerned with higher H\"older regularity for viscosity solutions to non-translation invariant second order integro-PDEs, compared to \cite{mou2018}. We first obtain $C^{1,\alpha}$ regularity estimates for fully nonlinear…