We show uniqueness results for the Dirichlet problem for YangMills connections defined in n-dimensional (n ≥ 4) star-shaped domains with flat boundary values. This result also shows the non-existence result for the Dirichlet problem in dimension 4, since in 4-dimension, there exist countably many connected components of connections with prescribed Dirichlet boundary value. We also show non-exis...

In this paper, we study delayed reactiondiffusion neural networks with general boundary conditions including Dirichlet and Neumann boundary conditions. By using some inequality techniques and constructing suitable Lyapunov functionals, some sufficient conditions are given to ensure the exponential synchronization of the drive-response neural networks. Finally, an example is given to verify the ...

This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the field is introduced. The fractional Neumann condition allows the interpolation of Dirichlet and Neumann conditions imposed on the two plates. There exists a tra...

We consider semilinear elliptic problems of the form ∆u+g(u) = f(x) with Neumann boundary conditions or ∆u + λ1u + g(u) = f(x) with Dirichlet boundary conditions, and we derive conditions on g and f under which an upper bound on the number of solutions can be obtained.

We discuss various issues concerning the behaviors near the boundary (σ = 0, π) and the midpoint (σ = π/2) of the open string coordinate X(σ) and its conjugate momentum P (σ) = −iδ/δX(σ) acting on the matter projectors of vacuum string field theory. Our original interest is in the dynamical change of the boundary conditions of the open string coordinate from the Neumann one in the translational...

In this note self-adjoint realizations of second order elliptic differential expressions with non-local Robin boundary conditions on a domain Ω ⊂ Rn with smooth compact boundary are studied. A Schatten–von Neumann type estimate for the singular values of the difference of the mth powers of the resolvents of two Robin realizations is obtained, and for m > n 2 − 1 it is shown that the resolvent p...

We prove sharp convergence rates for a class of domain embedding methods for elliptic boundary value problems. The theory is established for Dirichlet, Neumann, and Robin boundary conditions, and is unified in a new formulation for mixed boundary condition. On the continuous level, the methods for these boundary value problems perform equally well.

In this paper, we consider the controllability of the Korteweg-de Vries equation in a bounded interval when the control operates via the right Dirichlet boundary condition, while the left Dirichlet and the right Neumann boundary conditions are kept to zero. We prove that the linearized equation is controllable if and only if the length of the spatial domain does not belong to some countable cri...

In this paper, a method of separating variables is effectively implemented for solving a time-fractional telegraph equation (TFTE). We discuss and derive the analytical solution of the TFTE with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin boundary conditions. © 2007 Elsevier Inc. All rights reserved.

Part 2 continues the study of optimization techniques for elliptic control problems subject to control and state constraints and is devoted to distributed control. Boundary conditions are of mixed Dirichlet and Neumann type. Necessary conditions of optimality are formally stated in form of a local Pontryagin minimum principle. By introducing suitable discretization schemes, the control problem ...