Related papers: On some errors related to the graduation of measur…

The method of variational completion allows one to transform an (in principle, arbitrary) system of partial differential equations -- based on an intuitive ``educated guess'' -- into the Euler-Lagrange one attached to a Lagrangian, by…

Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the…

In this paper, we solve the $p$-Dirichlet problem for Besov boundary data on unbounded uniform domains with bounded boundaries when the domain is equipped with a doubling measure satisfying a Poincar\'{e} inequality. This is accomplished by…

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…

We consider equidistant Riemann approximations of stochastic integrals $\int_0^T f(B^H_s)dB^H_s$ with respect to the fractional Brownian motion with $H>\frac12$, where $f$ is an arbitrary function of locally bounded variation, hence…

We propose a new method to apply the Lipschitz functional calculus of local Dirichlet forms to Poisson random measures.

We introduce a class of Gaussian processes with stationary increments which exhibit long-range dependence. The class includes fractional Brownian motion with Hurst parameter H>1/2 as a typical example. We establish infinite and finite past…

The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…

The starting point is a gradient Dirichlet form with respect to $\varrho\lambda^d$ on the space $L^2({\mathbb{R}}^d, \varrho\mu)$. Here $\lambda^d$ is the Lebesgue measure on ${\mathbb R}^d$, $\varrho$ a strictly positive density and $\mu$…

We study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a $(1,1)$-Poincar\'e inequality.…

The paper presents theorems on the calculation of the index of a singular point and at the infinity of monotone type mappings. These theorems cover basic cases when the principal linear part of a mapping is degenerate. Applications of these…

Given a compact doubling metric measure space $X$ that supports a $2$-Poincar\'e inequality, we construct a Dirichlet form on $N^{1,2}(X)$ that is comparable to the upper gradient energy form on $N^{1,2}(X)$. Our approach is based on the…

In this note we study the Dirichlet problem associated with a version of prime end boundary of a bounded domain in a complete metric measure space equipped with a doubling measure supporting a Poincare inequality. We show the resolutivity…

We consider the problem of determining the boundary perturbations of an object from far-field electric or acoustic measurements. Assuming that the unknown object boundary is a small perturbation of a circle, we develop a linearized relation…

Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…

We prove a Donsker and a Glivenko--Cantelli theorem for sequences of random discrete measures generalizing empirical measures. Those two results hold under standard conditions upon bracketing numbers of the indexing class of functions. As a…

For the pure biharmonic equation and a biharmonic singular perturbation problem, a residual-based error estimator is introduced which applies to many existing nonconforming finite elements. The error estimator involves the local…

In this paper we prove Holder regularity of the gradient for solutions of Dirichlet problem associate to degenerate elliptic equations, extending the recent result of Imbert and Silvestre. Indeed we obtain regularity up to the boundary and…

This paper deals with the \emph{integral} version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the H\"older regularity of the data. By…

In this paper, a study of random times on filtered probability spaces is undertaken. The main message is that, as long as distributional properties of optional processes up to the random time are involved, there is no loss of generality in…