We introduce a new Neumann problem for the fractional Laplacian arising from a simple probabilistic consideration, and we discuss the basic properties of this model. We can consider both elliptic and parabolic equations in any domain. In addition, we formulate problems with nonhomogeneous Neumann conditions, and also with mixed Dirichlet and Neumann conditions, all of them having a clear probab...

In the context of the bulk-boundary correspondence we study the correlation functions arising on a boundary for different types of boundary conditions. The most general condition is the mixed one interpolating between the Neumann and Dirichlet conditions. We obtain the general expressions for the correlators on a boundary in terms of Green’s function in the bulk for the Dirichlet, Neumann and m...

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)...

This paper shows that the time t map of the averaged Euler equations, with Dirichlet, Neumann, and mixed boundary conditions is canonical relative to a Lie-Poisson bracket constructed via a non-smooth reduction for the corresponding diffeomorphism groups. It is also shown that the geodesic spray for Neumann and mixed boundary conditions is smooth, a result already known for Dirichlet boundary c...

Let M be a compact Riemannian manifold with boundary ∂M and L = ∆+ Z for a C1-vector field Z on M . Several equivalent statements, including the gradient and Poincaré/log-Sobolev type inequalities of the Neumann semigroup generated by L, are presented for lower bound conditions on the curvature of L and the second fundamental form of ∂M . The main result not only generalizes the corresponding k...

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...