We prove existence of solutions and study the nonlocal-to-local asymptotics for nonlocal, convective, Cahn-Hilliard equations in case a W^{1,1} convolution kernel under homogeneous Neumann conditions. Any type potential, possibly also double-obstacle or logarithmic type, is included. Additionally, we highlight variants extensions to setting periodic boundary conditions viscosity contributions, ...

This paper considers interactions between closed strings and open strings satisfying either Neumann or constant (point-like) Dirichlet boundary conditions in a BRST formalism in the critical dimension. With Neumann conditions this reproduces the well-known stringy version of the Higgs mechanism. With Dirichlet conditions the open-string states correspond to either auxiliary or Lagrange multipli...

We study a bifurcation problem for the equation ∆u+λu+ g(λ, u) = 0 on a rectangle with Signorini boundary conditions on a part of one edge and mixed (zero Dirichlet and Neumann) boundary conditions on the rest of the boundary. Here λ ∈ R is the bifurcation parameter, and g is a small perturbation. Under certain assumptions concerning an eigenfunction u0 corresponding to an eigenvalue λ0 of the ...

Let M be a compact Riemannian manifold with smooth boundary. We obtain the exact long time asymptotic behaviour of heat kernel on abelian coverings mixed Dirichlet and Neumann boundary conditions. As an application, we study abelianized winding reflected Brownian motions in M. In particular, prove Gaussian type central limit theorem showing that when rescaled appropriately, fluctuations are nor...

We investigate a nonstandard phase field model of Cahn-Hilliard type. The model, which was introduced in [16], describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in [5], [6] for the case of homogeneous Neumann boundary conditions. In this paper, we investigate the case that the boundary condition for one of the u...

This paper is devoted to some elliptic boundary value problems in a self-similar ramified domain of R with a fractal boundary. Both the Laplace and Helmholtz equations are studied. A generalized Neumann boundary condition is imposed on the fractal boundary. Sobolev spaces on this domain are studied. In particular, extension and trace results are obtained. These results enable the investigation ...