We construct quantum effective action in spacetime with branes/boundaries. This construction is based on the reduction of the underlying Neumann type boundary value problem for the propagator of the theory to that of the much more manageable Dirichlet problem. In its turn, this reduction follows from the recently suggested Neumann-Dirichlet duality which we extend beyond the tree level approxim...

In this paper, we study the shape optimization problem for first eigenvalue of p-Laplace operator with mixed Neumann-Dirichlet boundary conditions on multiply-connected domains in hyperbolic space. Precisely, establish that among all a given volume and prescribed (n−1)-th quermassintegral convex Dirichlet (inner boundary), concentric annular region produces largest eigenvalue. We also derive Na...

We define and study the properties of Darboux-type transformations between Sturm–Liouville problems with boundary conditions containing rational Herglotz–Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary conditions). Using these transformations, we obtain various direct and inverse spectral results for these problems in a unified manner, such as asymptotics of e...

In this work we show the application of the Method of Fundamental Solutions (MFS) in the determination of eigenfrequencies and eigenmodes associated to wave scattering problems. This meshless method has already been applied to simple geometry domains with Dirichlet boundary conditions (e.g. [8]). Here we show that a particular choice of point-sources can lead to very good results for a fairly g...

In this paper, we study the spectral theory for nonlocal dispersal operators with time periodic indefinite weight functions subject to Dirichlet type, Neumann type and spatial periodic type boundary conditions. We first obtain necessary and sufficient conditions for the existence of a unique positive principal spectrum point for such operators. We then investigate upper bounds of principal spec...

The stationary Boussinesq equations describing the heat transfer in the viscous heat-conducting fluid under inhomogeneous Dirichlet boundary conditions for velocity and mixed boundary conditions for temperature are considered. The optimal control problems for these equations with tracking-type functionals are formulated. A local stability of the concrete control problem solutions with respect t...

Using a new local smoothing estimate of the first and third authors, we prove local-in-time Strichartz and smoothing estimates without a loss exterior to a large class of polygonal obstacles with arbitrary boundary conditions and global-in-time Strichartz estimates without a loss exterior to a large class of polygonal obstacles with Dirichlet boundary conditions. In addition, we prove a global-...

In this paper, we consider an acoustic wave transmission problem with mixed boundary conditions of Dirichlet, Neumann, and impedance type. We will derive a formulation as direct, space-time retarded integral equation, where both Cauchy data are kept unknowns on the part boundary. This requires definition single-trace spaces which incorporate homogeneous Dirichlet Neumann corresponding parts pro...

We investigate stability properties of indirectly damped systems of evolution equations in Hilbert spaces, under new compatibility assumptions. We prove polynomial decay for the energy of solutions and optimize our results by interpolation techniques, obtaining a full range of power-like decay rates. In particular, we give explicit estimates with respect to the initial data. We discuss several ...

where t ≥ 0 denotes time and x ∈ Ω ⊂ R position typical within a d−dimensional bounded domain Ω with “sufficiently smooth” boundary or Ω = R. The states u = (u1, . . . , um), i = 1, . . . , m describe the concentrations or densities of substances/populations ui = ui(t, x). The functions di(t, x) are called diffusion coefficients or diffusivities. On a bounded domain Ω the eqs. (1) have to be co...