Related papers: Wiener criterion for X-elliptic operators
Wiener's criterion for the regularity of a boundary point with respect to the Dirichlet problem for the Laplace equation has been extended to various classes of elliptic and parabolic partial differential equations. They include linear…
We study the boundary continuity of solutions to fully nonlinear elliptic equations. We first define a capacity for operators in non-divergence form and derive several capacitary estimates. Secondly, we formulate the Wiener criterion, which…
We study the boundary behavior of solutions to the Dirichlet problems for integro-differential operators with order of differentiability $s \in (0, 1)$ and summability $p>1$. We establish a nonlocal counterpart of the Wiener criterion,…
We study the Dirichlet problem for a second-order elliptic operator $L^*$ in double divergence form, also known as the stationary Fokker-Planck-Kolmogorov equation. Assuming that the leading coefficients have Dini mean oscillation, we…
In this paper, we prove Wiener's criterion for parabolic equations with singular and degenerate coefficients. To be precise, we study the problem of the regularity of boundary points for the Dirichlet problem for degenerate parabolic…
We establish a necessary and sufficient condition for a boundary point to be regular for the Dirichlet problem related to a class of Kolmogorov-type equations. Our criterion is inspired by two classical criteria for the heat equation: the…
In this paper we are concerned with hypoelliptic diffusion operators $\mathcal{H}$. Our main aim is to show, with an axiomatic approach, that a Wiener-type test of $\mathcal{H}$-regularity of boundary points can be derived starting from the…
We study boundary regularity at the infinity point $\boldsymbol{\infty}$ for nonlinear elliptic equations of $p$-Laplace type in unbounded open sets $\Omega \subset \mathbf{R}^n$. We consider the case $p \ge n \ge 2$ and characterize the…
We consider the Dirichlet problem for quasilinear elliptic equations with Musielak-Orlicz (p,q)-growth and non-logarithmic conditions on the coefficients. A sufficient Wiener-type condition for the regularity of a boundary point is…
The primary purpose of this paper is to study the Wiener-type regularity criteria for non-linear equations driven by integro-differential operators, whose model is the fractional $p-$Laplace equation. In doing so, with the help of tools…
The theory of second order complex coefficient operators of the form $\mathcal{L}=\mbox{div} A(x)\nabla$ has recently been developed under the assumption of $p$-ellipticity. In particular, if the matrix $A$ is $p$-elliptic, the solutions…
This paper investigates the Dirichlet problem for a non-divergence form elliptic operator $L$ in a bounded domain of $\mathbb{R}^d$. Under certain conditions on the coefficients of $L$, we first establish the existence of a unique Green's…
This paper introduces a notion of regularity (or irregularity) of the point at infinity for the unbounded open subset of $\rr^{N}$ concerning second order uniformly elliptic equations with bounded and measurable coefficients, according as…
The present paper establishes a certain duality between the Dirichlet and Regularity problems for elliptic operators with $t$-independent complex bounded measurable coefficients ($t$ being the transversal direction to the boundary). To be…
In this paper we prove a Wiener-type characterization of boundary regularity, in the spirit of a classical result by Landis, for a class of evolutive H\"ormander operators. We actually show the validity of our criterion for a larger class…
The model problem of a plane angle for a second-order elliptic system subject to Dirichlet, mixed, and Neumann boundary conditions is analyzed. For each boundary condition, the existence of solutions of the form $r^\lambda v$ is reduced to…
In the framework of Potential Theory we prove existence or the Perron-Weiner-Brelot-Bauer solution to the Dirichlet problem related to a family of totally degenerate, in the sense of Bony, differential operators. We also state and prove a…
In this article, we present a simpler and alternative proof of the solvability of the regularity problem - that is, the Dirichlet problem with boundary data in $\dot W^{1,p}$ - for uniformly elliptic operators on $\mathbb{R}^n_+$ under a…
In this paper we establish of the Wiener criterion for solution the mixed boundary problem for nonlinear elliptic equation of second order.
This Note derives regularity bounds for a Gevrey criterion when the Cauchy problem of elliptic equations is solved by regularization. When utilizing the regularization, one knows that checking such criterion is basically problematic, albeit…