Related papers: Elliptic boundary value problems for the stationar…
In this paper second order elliptic boundary value problems on bounded domains $\Omega\subset\dR^n$ with boundary conditions on $\partial\Omega$ depending nonlinearly on the spectral parameter are investigated in an operator theoretic…
This article proves the well posedness of the boundary value problemthat arises when PML algorithms are applied to Pauli's equationswith a three dimensional rectangle as computational domain. The absorptionsare positive near the boundary…
We study elliptic equations on bounded domain of Euclidean spaces in the variable H\"{o}lder spaces. Interior a priori Schauder estimates are given as well as global ones. Moreover, the existence and the uniqueness of solutions to the…
We investigate the Bartnik stationary extension conjecture, which arises from the definition of the spacetime Bartnik mass for a compact region in a general initial data set satisfying the dominant energy condition. This conjecture posits…
We use novel integral representations developed by the second author to prove certain rigorous results concerning elliptic boundary value problems in convex polygons. Central to this approach is the so-called global relation, which is a…
We find that for various solitonic processes the corresponding canonical moduli space can have a boundary which is accessible in a finite time evolution. We show that such a boundary is not a failure of the moduli space approach but has a…
We consider shape optimization problems for general integral functionals of the calculus of variations that may contain a boundary term. In particular, this class includes optimization problems governed by elliptic equations with a Robin…
The inviscid multi-layer quasi-geostrophic equations are considered over an arbitrary bounded domain. The no-flux but non-homogeneous boundary conditions are imposed to accommodate the free fluctuations of the top and layer interfaces.…
In a class of inner product H\"ormander spaces, we investigate a general elliptic problem for which the maximum of orders of boundary conditions is grater than or equal to the order of elliptic equation. The order of regularity for these…
Recent work in Euclidean quantum gravity has studied boundary conditions which are completely invariant under infinitesimal diffeomorphisms on metric perturbations. On using the de Donder gauge-averaging functional, this scheme leads to…
We investigate an arbitrary regular elliptic boundary-value problem given in a bounded Euclidean domain with infinitely smooth boundary. We prove that the operator of the problem is bounded and Fredholm in appropriate pairs of H\"ormander…
We study linear and quasilinear Venttsel boundary value problems involving elliptic operators with discontinuous coefficients. On the base of the a priori estimates obtained, maximal regularity and strong solvability in Sobolev spaces are…
We investigate the realization of a myriad of general local and nonlocal inhomogeneous elliptic and parabolic boundary value problems over classes of irregular regions. We present a unified approach in which either local or nonlocal…
The paper presents a first step towards a family index theorem for classical self-adjoint boundary value problems. We address here the simplest non-trivial case of manifolds with boundary, namely the case of two-dimensional manifolds. The…
We demonstrate how the solution to an exterior Dirichlet boundary value problem of the axisymmetric, stationary Einstein equations can be found in terms of generalized solutions of the Backlund type. The proof that this generalization…
We provide a formulation of the initial boundary value problem for Friedrich's extended conformal Einstein field equations in which boundary data is prescribed on a timelike hypersurface located at a finite position in the spacetime. Our…
A generalization of the notion of ellipsoids to curved Riemannian spaces is given and the possibility to use it in describing the shapes of rotating bodies in general relativity is examined. As an illustrative example, stationary,…
We consider an elliptic boundary problem over a bounded region $\Omega$ in $\mathbb{R}^n$ and acting on the generalized Sobolev space $W^{0,\chi}_p(\Omega)$ for $1 < p < \infty$. We note that similar problems for $\Omega$ either a bounded…
Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary…
We consider a boundary value problem of a stationary advection equation in a bounded domain with Lipschitz boundary. It is known to be well-posed in $L^p$-based function spaces for $1 < p < \infty$ under the separation condition of the…