Related papers: Something about Poisson and Dirichlet

In this paper, we proceed to develop a new approach which was formulated first in Ershkov (2017) for solving Poisson equations: a new type of the solving procedure for Euler-Poisson equations (rigid body rotation over the fixed point) is…

In this paper we study the Perron method for solving the p-harmonic Dirichlet problem on the topologist's comb. For functions which are bounded and continuous at the accessible points, we obtain invariance of the Perron solutions under…

A standard Hilbert-space proof of Dirichlet's principle is simplified, using an observation that a certain form of min-problem has unique solution, at a specified point. This solves Dirichlet's problem, after it is recast in the required…

Unidirectional flow is the simplest phenomenon of fluid mechanics. Its mathematical description, the Dirichlet problem for Poisson's equation in two dimensions with constant forcing, arises in many physical contexts, such as the torsion of…

This paper investigates lower bounds on the number of zeros and poles of a general Dirichlet series in a disk of radius $r$ and gives, as a consequence, an affirmative answer to an open problem of Bombieri and Perelli on the bound.…

We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…

This paper is devoted to Riemann-Hilbert problems with constraints. We obtain results characterizing the existence of solutions as well as the dimension of the solution space in terms of certain indices. As an application, we show how such…

In this paper, we study the Poisson problem involving a fractional Hardy operator and a measure source. The complex interplay between the nonlocal nature of the operator, the peculiar effect of the singular potential and the measure source…

We study the Dirichlet problem for semilinear equations on general open sets with measure data on the right-hand side and irregular boundary data. For this purpose we develop the classical method of orthogonal projection. We treat in a…

The main result establishes the existence of a solution in a generalized sense for a nonlinear Dirichlet problem driven by a competing operator and exhibiting a convection term composed with an intrinsic operator. A finite dimensional…

The compound decision problem for a vector of independent Poisson random variables with possibly different means has half a century old solution. However, it appears that the classical solution needs smoothing adjustment even when there are…

The purpose of this paper is to prove directly, by an elementary method, the Poisson probability law. This proof is offered as an alternative to the more usual derivation from binomial distribution in the limit of small probabilities. The…

We generalize Dahmen-Micchelli deconvolution formula for Box splines with parameters. Our proof is based on identities for Poisson summation of rational functions with poles on hyperplanes.

We study the convergence of the Method of Reflections for the Dirichlet problem of the Poisson and the Stokes equations in perforated domains which consist in the exterior of balls. We prove that the method converges if the balls are…

We will find Green's function for the standard weighted Laplacian and use the corresponding Green's potential to solve Poisson's equation in the unit disc with zero boundary values, in the sense of radial $L^1$-means, for complex Borel…

A compact semisimple Lie algebra $\mathfrak{g}$ induces a Poisson structure $\pi$ on the unit sphere $S$ in $\mathfrak{g}^*$. We compute the moduli space of Poisson structures on $S$ around $\pi$. This is the first explicit computation of a…

For elliptic in the half-space and parabolic degenerating on the boundary equation of Keldysh type we construct by similarity method the self-similar solution, which is the approximation to the identity in the class of integrable functions.…

In this paper, we consider the Dirichlet problem for a new class of augmented Hessian equations. Under sharp assumptions that the matrix function in the augmented Hessian is regular and there exists a smooth subsolution, we establish global…

We use Poisson summation formula to calculate integrals of producs of sinc functions (cf. [4]) and related integrals as in [5] and [3]. We also generalize the one in [5] and introduce other remarkable integrals. Finally we give a sum…

The theory of orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to functional-difference…