Related papers: Some remarks on uniform boundary Harnack Principle…
We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…
We prove an uniform boundary Harnack inequality for nonnegative functions harmonic with respect to $\alpha$-stable process on the Sierpi{\'n}ski triangle, where $\alpha \in (0, 1)$. Our result requires no regularity assumptions on the…
We study the stability of John domains in Banach spaces under removal of a countable set of points. In particular, we prove that the class of John domains is stable in the sense that removing a certain type of closed countable set from the…
It is common knowledge that the Einstein-Hilbert action does not furnish a well-posed variational principle. The usual solution to this problem is to add an extra boundary term to the action, called a counter-term, so that the variational…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
It is known that if X is uniformly distributed modulo 1 and Y is an arbitrary random variable independent of X then Y+X is also uniformly distributed modulo 1. We prove a converse for any continuous random variable Y (or a reasonable…
Let $G$ be a nonempty bounded domain in a finite-dimensional Euclidean space. The main results are general estimates from below at points from $G$ for an arbitrary subharmonic function $u\not\equiv -\infty$ on the closure of the domain $G$…
We consider Borwein-Preiss and Ekeland variational principles using distance functions that neither is symmetric nor enjoy the triangular inequality. All the given results rely exclusively on the convergence and continuity behaviors induced…
We consider the behavior of the nonlocal minimal surfaces in the vicinity of the boundary. By a series of detailed examples, we show that nonlocal minimal surfaces may stick at the boundary of the domain, even when the domain is smooth and…
The manuscript contains elegant extensions of the fundamental variational principles: Br\o ndsted's and Ekeland's. On the other hand we get general and precise version of the Takahashi and the Cariste fixed point theorems. The results are…
The article provides proofs for the regularity of Dirac eigenfunctions, subject to MIT boundary conditions employed on various types of open sets ranging from smooth ones to convex polygons in two dimensions, as well as on half-space and…
A uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains is established. Exact Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are given. Extensions…
We present a slightly different formulation of Zak's theorem on tangencies as well as some applications. In particular, we obtain a better bound on the dimension of the dual variety of a manifold and we classify extremal and…
The aim of this paper is to investigate the well-posedness of a class of boundary control and observation systems on a one dimensional spatial domain. We derive a necessary and sufficient condition characterizing the well-posedness of these…
We develop a new, unified approach to the following two classical questions on elliptic PDE: the strong maximum principle for equations with non-Lipschitz nonlinearities, and the at most exponential decay of solutions in the whole space or…
The aim of this paper is first to give necessary and sufficient condition of existence (of free boundaries) for both Laplacian and bi-Laplacian operators in the case where the overdetermined condition is not constant. second, by using some…
We obtain free of resonances regions for the elasticity system in the exterior of a strictly convex body with dissipative boundary conditions under some natural assumptions on the behaviour of the geodesics on the boundary.
We consider two simple models of higher-derivative and nonlocal quantu systems.It is shown that, contrary to some claims found in literature, they can be made unitary.
This paper proposes new tests of conditional independence of two random variables given a single-index involving an unknown finite-dimensional parameter. The tests employ Rosenblatt transforms and are shown to be distribution-free while…
A monotonicity property of Harnack inequality is proved for positive invariant harmonic functions in the unit ball.