相关论文: On the Dirichlet problem for asymmetric zero-range…

We study the invariant measures and fluctuation limits of discrete-time harness processes in one spatial dimension. We construct one essential ergodic (under spatial shifts) invariant measure of the increment process derived from harness…

We investigate the effects of advection on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions. Various asymptotic behaviors of the principal eigenvalues, when advection coefficient…

Given a smooth bounded domain ${\O}\subseteq \R^2$, we consider the equation $\D v = 2 v_x \wedge v_y$ in $\O$, where $v: {\O}\to \R^3$. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An…

In this paper we establish new renormalized oscillation theorems for discrete symplectic eigenvalue problems with Dirichlet boundary conditions. These theorems present the number of finite eigenvalues of the problem in arbitrary interval…

We consider a class of nonlinear integro-differential operators and prove existence of two principal (half) eigenvalues in bounded smooth domains with exterior Dirichlet condition. We then establish simplicity of the principal…

In this paper we consider a family of non local functionals of convolution-type depending on a small parameter $\varepsilon>0$ and $\Gamma$-converging to local functionals defined on Sobolev spaces as $\varepsilon\to 0$. We study the…

A system of boundary-domain integral equations is derived from the bidimensional Dirichlet problem for the diffusion equation with variable coefficient using the novel parametrix from [22] different from the one in [5,18]. Mapping…

A nonuniform Neumann boundary-value problem is considered for the Poisson equation in a thin domain $\Omega_\varepsilon$ coinciding with two thin rectangles connected through a joint of diameter ${\cal O}(\varepsilon)$. A rigorous procedure…

After recalling basic features of the theory of symmetric quasi regular Dirichlet forms we show how by applying it to the stochastic quantization equation, with Gaussian space-time noise, one obtains weak solutions in a large invariant set.…

This is the second in a series of works devoted to small non-selfadjoint perturbations of selfadjoint semiclassical pseudodifferential operators in dimension 2. As in our previous work, we consider the case when the classical flow of the…

A connection between the semigroup of the Cauchy process killed upon exiting a domain $D$ and a mixed boundary value problem for the Laplacian in one dimension higher known as the "mixed Steklov problem," was established in a previous paper…

We study the Dirichlet boundary value problem for viscoelastic diffusion in polymers. We show that its weak solutions generate a dissipative semiflow. We construct the minimal trajectory attractor and the global attractor for this problem.

This work considers the Neumann eigenvalue problem for the weighted Laplacian on a Riemannian manifold $(M,g,\partial M)$ under the singular perturbation. This perturbation involves the imposition of vanishing Dirichlet boundary conditions…

Using, as main tool, the convergence theorem for discrete martingales and the mean value property of harmonic functions we solve, a particular case of, Dirichlet problem.

We solve the nonlinear Dirichlet problem (uniquely) for functions with prescribed asymptotic singularities at a finite number of points, and with arbitrary continuous boundary data, on a domain in euclidean space. The main results apply, in…

In this paper, we study boundary-value problems describing the exit distribution of finite-velocity random motions from prescribed domains. For the standard telegraph process, with and without drift, we derive the Dirichlet problems…

We study a discrete and continuous version of the spectral Dirichlet problem in an open bounded connected set $\Omega\subset \mathbb{R}^d$, in dimension $d\geq 2$. More precisely, consider the simple random walk on $\mathbb{Z}^d$ killed…

We consider the Dirichlet and Neumann eigenvalues of the Laplacian for a planar, simply connected domain. The eigenvalues admit a characterization in terms of a layer potential of the Helmholtz equation. Using the exterior conformal mapping…

We consider the Laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for…

We propose a new approach for finding discrete harmonic functions in the quarter plane with Dirichlet conditions. It is based on solving functional equations that are satisfied by the generating functions of the values taken by the harmonic…