We develop a general variational framework for the finite element solution of the pure Neumann problem. Our starting point is the equivalence between the weak Neumann equation and a minimization problem on the factor space H1(Ω)/RI . This problem gives rise to a family of minimization problems posed on conventional Sobolev spaces but constrained by a generalized zero-mean condition. We show tha...

A method for explicitly solving the exterior Dirichlet problem for the threedimensional Helmholtz equation in terms of the Dirichlet Green's function for Laplace's equation has recently been found [6]. The present work shows how a similar technique may be used to solve the exterior Neumann problem in terms of the corresponding Neumann-Green function for Laplace's equation. The existence of the ...

We prove that it is not possible to classify separable von Neumann factors of types II1, II∞ or IIIλ, 0 ≤ λ ≤ 1, up to isomorphism by a Borel measurable assignment of “countable structures” as invariants. In particular the isomorphism relation of type II1 factors is not smooth. We also prove that the isomorphism relation for von Neumann II1 factors is analytic, but is not Borel.

We study the ∂̄b-Neumann problem for domains Ω contained in a strictly pseudoconvex manifold M2n+1 whose boundaries are noncharacteristic and have defining functions depending solely on the real and imaginary parts of a single CR function w. When the Kohn Laplacian is a priori known to have closed range in L2, we prove sharp regularity and estimates for solutions. We establish a condition on the...

this paper is concerned with a 2nth-order p-laplacian difference equation. by using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for neumann boundary value problem and give some new results. results obtained successfully generalize and complement the existing ones.

The paper analyzes a continuous and discrete version of the Neumann-Neumann domain decomposition algorithm for two-body contact problems with Tresca friction. Each iterative step consists of a linear elasticity problem for one body with displacements prescribed on a contact part of the boundary and a contact problem with Tresca friction for the second body. To ensure continuity of contact stres...

The BEM is applied to the solution of the torsion problem of non-homogeneous anisotropic non-circular prismatic bars. The problem is formulated in terms of the warping function. This formulation leads to a second order partial differential equation with variable coefficients, subjected to a generalized Neumann type boundary condition. The problem is solved using the Analog Equation Method (AEM)...

The purpose of this note is to bring update results on boundary value problems on Lipschitz domains in R or C. We first discuss the Dirichlet problem, the Neumann problem and the d-Neumann problem in a bounded domain in R. These problems are the prototypes of coercive (or elliptic ) boundary value problems when the boundary of the domain is smooth. When the domain is only Lipschitz, solutions t...

We consider a reaction-diffusion equation with Neumann boundary conditions and show that solutions to this problem may be obtained from a problem with periodic boundary conditions and equivariant under O(2) symmetry. We describe the solutions for Hopf bifurcation and mode interactions involving Hopf bifurcation, namely, steadystate/Hopf and Hopf/Hopf. Neumann boundary conditions constrain the s...