It is well-known that the Dirichlet problem for the MongeAmpère equation det Du = μ in a bounded strictly convex domain Ω in R has a weak solution (in the sense of Aleksandrov) for any finite Borel measure μ on Ω and for any continuous boundary data. We consider the Dirichlet problem when Ω is only assumed to be convex, and give a necessary and sufficient condition on the boundary data for solv...

Dirichlet-branes have emerged as important objects in studying nonperturbative string theory. It is important to generalize these objects to more general backgrounds other than the usual flat background. The simplest case is the linear dilaton condensate. The usual Dirichlet boundary condition violates conformal invariance in such a background. We show that by switching on a certain boundary in...

We present an algorithm for characterising the generalised Dirichlet to Neumann map for moving initial-boundary value problems. This algorithm is derived by combining the so-called global relation, which couples the initial and boundary values of the problem, with a new method for inverting certain one-dimensional integrals. This new method is based on the spectral analysis of an associated ODE...

Casimir forces are conventionally computed by analyzing the effects of boundary conditions on a fluctuating quantum field. Although this analysis provides a clean and calculationally tractable idealization, it does not always accurately capture the characteristics of real materials, which cannot constrain the modes of the fluctuating field at all energies. We study the vacuum polarization energ...

This paper develops a framework to include Dirichlet boundary conditions on a subset of the boundary which depends on time. In this model, the boundary conditions are weakly enforced with the help of a Lagrange multiplier method. In order to avoid that the ansatz space of the Lagrange multiplier depends on time, a bi-Lipschitz transformation, which maps a fixed interval onto the Dirichlet bound...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 28 September 2020Accepted: 2021Published online: 14 February 2022Keywordssemiclassical limit, Schrödinger equation, boundary layer, successive complementary expansion methodAMS Subject Headings35Q40, 35Q55Publication DataISSN (print): 0036-1410ISSN (online): 1095-7154Publ...

where T ≥ 2 is a positive integer andΔu k u k 1 −u k is the forward difference operator. Throughout this paper, we denote by Z a, b the discrete interval {a, a 1, . . . , b}, where a and b are integers and a < b. We consider in 1.1 two different boundary conditions: a Dirichlet boundary condition u 0 0 and a Neumann boundary condition Δu T 0 . In the literature, the boundary condition considere...