Related papers: Probabilistic Solution of the General Robin Bounda…
In this paper, we propose numerical methods for computing the boundary local time of reflecting Brownian motion (RBM) in R3 and its use in the probabilistic representation of the solution of the Laplace equation with the Neumann boundary…
We develop methods for the solution of inhomogeneous Robin type boundary value problems (BVPs) that arise for certain linear parabolic Partial Differential Equations (PDEs) on a half line, as well as a second order generalisation. We are…
It is developed the theory of the boundary behavior of homeomorphic solutions of the Beltrami equations ${\bar{\partial}}f=\mu\,{\partial}f$ of the Sobolev class $W^{1,1}_{\rm loc}$ with respect to prime ends of domains. On this basis,…
We study a counterpart of the classical Poisson integral for a family of weighted Laplace differential equations in Euclidean half space, solutions of which are known as generalized axially symmetric potentials. These potentials appear…
We consider the Poisson equation with homogeneous Dirichlet conditions in a family of domains in $R^{n}$ indexed by a small parameter $\epsilon$. The domains depend on $\epsilon$ only within a ball of radius proportional to $\epsilon$ and,…
The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…
Let $\Omega\subset \mathbb R^2$ be a bounded planar domain, with piecewise smooth boundary $\partial \Omega$. For $\sigma>0$, we consider the Robin boundary value problem \[ -\Delta f =\lambda f, \qquad \frac{\partial f}{\partial n} +…
We prove \emph{uniform solvability estimates} for certain families of elliptic problems posed in a bounded family of domains (for example, a sequence that converges to another domain). We provide uniform estimates both in weighted and in…
This work reformulates the complete electrode model of electrical impedance tomography in order to enable more efficient numerical solution. The model traditionally assumes constant contact conductances on all electrodes, which leads to a…
A simple-to-implement weak-sense numerical method to approximate reflected stochastic differential equations (RSDEs) is proposed and analysed. It is proved that the method has the first order of weak convergence. Together with the Monte…
In this paper we consider a Robin problem for the Klein-Gordon equation in a doubly connected domain. The solution domain considered is a bounded smooth doubly connected planar domain bounded by two simple disjoint closed curves. The…
We study the Dirichlet boundary value problem for equations with absorption of the form $-\Delta u+g\circ u=\mu$ in a bounded domain $\Omega\subset R^N$ where $g$ is a continuous odd monotone increasing function. Under some additional…
We consider elliptic equations and systems in divergence form with the conormal or the Robin boundary conditions, with small BMO (bounded mean oscillation) or variably partially small BMO coefficients. We propose a new class of domains…
We consider a boundary value problem for a general second order linear equation in a domain with a fine perforation. The latter is made by small cavities; both the shapes of the cavities and their distribution are arbitrary. The boundaries…
We study an inverse boundary value problem associated with $p$-Laplacian which is further perturbed by a linear second order term, defined on a bounded set $\Omega$ in $\R^n, n\geq 2$. We recover the coefficients at the boundary from the…
Linear second order elliptic boundary value problems (BVP) on bounded Lipschitz domains are studied in the case of Gaussian white noise loads. Especially, Neumann and Robin BVPs are considered. The main obstacle for applying the usual…
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…
In this paper second order elliptic boundary value problems on bounded domains $\Omega\subset\dR^n$ with boundary conditions on $\partial\Omega$ depending nonlinearly on the spectral parameter are investigated in an operator theoretic…
We prove the existence of unique solutions to the Dirichlet boundary value problems for linear second-order uniformly parabolic operators in either divergence or non-divergence form with boundary blowup low-order coefficients. The domain is…
Robin problem for the Laplacian in a bounded planar domain with a smooth boundary and a large parameter in the boundary condition is considered. We prove a two-sided three-term asymptotic estimate for the negative eigenvalues. Furthermore,…