In this paper we study existence, uniqueness and solution estimates to the mixed problem r ru = 0 with Dirichlet to Neumann map boundary conditions and Neumann boundary conditions. We then show how this can be used in the reconstruction of , given the relationship between u and its normal derivative on the boundary portion where we do not apply the Dirichlet to Neumann map. A numerical reconstr...

We consider the wave equation in an unbounded conical domain, with initial conditions and boundary conditions of Dirichlet or Neumann type. We give a uniform decay estimate of the solution in terms of weighted Sobolev norms of the initial data. The decay rate is the same as in the full space case.

Recent work in the literature has proposed the use of non-local boundary conditions in Euclidean quantum gravity. The present paper studies first a more general form of such a scheme for bosonic gauge theories, by adding to the boundary operator for mixed boundary conditions of local nature a 2× 2 matrix of pseudo-differential operators with pseudo-homogeneous kernels. The request of invariance...

We consider Laplacian in a planar strip with Dirichlet boundary condition on the upper boundary and with frequent alternation boundary condition on the lower boundary. The alternation is introduced by the periodic partition of the boundary into small segments on which Dirichlet and Neumann conditions are imposed in turns. We show that under the certain condition the homogenized operator is the ...

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-...

Consider the eigenvalue problem generated by a fixed differential operator with sign-changing weight on term. We prove that as part of is rescaled towards negative infinity some subregion, spectrum converges to original restricted complementary region. On interface between regions limiting acquires Dirichlet-type boundary conditions. Our main theorem concerns problems for bilinear forms Hilbert...

In this work we derive the structural properties of the Collocation coefficient matrix associated with the Dirichlet-Neumann map for Laplace’s equation on a square domain. The analysis is independent of the choice of basis functions and includes the case involving the same type of boundary conditions on all sides, as well as the case where different boundary conditions are used on each side of ...

Our domain G = (0,L) is an interval of length L. The boundary ∂G = {0,L} are the two endpoints. We consider here as an example the case (DD) of Dirichlet boundary conditions: Dirichlet conditions at x = 0 and x = L. For other boundary conditions (NN), (DN), (ND) one can proceed similarly. In one dimension the Laplace operator is just the second derivative with respect to x: ∆u(x, t) = uxx(x, t)...

We give an example of an indefinite weight Sturm-Liouville problem whose eigenfunctions form a Riesz basis under Dirichlet boundary conditions but not under anti-periodic boundary conditions.