A boundary value problem for certain elliptic operators in the comple ment of an in nite cylinder is studied We prove that for these operators P D with some general zero boundary conditions if P D u has support inside a cylinder and decays exponentially in one direction of the cylinder then the solution u under a certain strong radiation condition at in nity must have support inside the cylinde...

Let Ω ⊂ RN with N ≥ 2. We consider the equations N ∑ i=1 ui ∂2u ∂xi + p(x) = 0, u|∂Ω = 0, with a1 ≥ a2 ≥ .... ≥ aN ≥ 0 and a1 > aN . We show that if Ω is a convex bounded region in RN , there exists at least one classical solution to this boundary value problem. If the region is not convex, we show the existence of a weak solution. Partial results for the existence of classical solutions for no...

The study ofmultipoint boundary value problem for linear second-order ordinary differential equation was initiated by I1’in and Moiseev 1 motivated by the work of Bitsadze and Samarskiı̆ 2–4 on nonlocal linear elliptic boundary value problem, which is a new area of still fairly theoretical exploration inmathematics. Several authors have expounded on various aspects of this theory; see the survey...

and reducing the problem to one of iteratively solving a linear equation for un once the previous iterates have been determined. However, Adomian partitions (1.4) into a sequence of linear ODEs in either x or t whose solutions cannot generally be made to satisfy the boundary and initial conditions. Even when applied to an initial value problem with boundary conditions, the convergence of the so...

In this article we study the scaling limit of interface model on \({{\,\mathrm{{\mathbb {Z}}}\,}}^d\) where Hamiltonian is given by a mixed gradient and Laplacian interaction. We show that in any dimension Gaussian free field. discuss appropriate spaces which convergence takes place. While infinite volume proof based Fourier analytic methods, finite rely some discrete PDE techniques involving f...

In this article, we study the elliptic boundary value problem −∆u + a(x)u = g(x, u) in Ω,

We study the elliptic boundary-value problem ∆u+ g(x, u) = p(x) in Ω u ∣∣ ∂Ω = constant, ∫