Related papers: Coarse homotopy theory and boundary value problems
In this paper we show that there is a well defined modified dbar-Neumann problem for a spin_c manifold with a strictly pseudoconvex boundary (in the contact geometry sense). We show that the index of the associated boundary value problem…
This paper is concerned with {an extension and reinterpretation} of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. {We state} two general abstract results on…
We investigate the problem of calculating the Fredholm index of a geometric Dirac operator subject to local (e.g. Dirichlet and Neumann) and non-local (APS) boundary conditions posed on the strata of a manifold with corners. The boundary…
We consider the coarse-geometric notion of ends in the context of coarse homotopy. We show that, when recontextualized as a functor from an appropriate coarse category of proper geodesic spaces, the set of ends $\mathcal{E}\text{nds}(-)$ is…
In this paper, we discuss the existence and uniqueness of solutions of a boundary value problem for a fractional differential equation of order $\alpha\in(2,3)$, involving a general form of fractional derivative. First, we prove an…
We interpret the coarse symbol and index class of a Callias type Dirac operator $D+\Psi$ on a manifold $M$ as a pairing between the coarse symbol and index classes associated to $D$ and K-theory classes of the coarse corona of $M$ or $M$…
In this paper we make a subtle use of operator theory techniques and the well-known Schauder fixed-point principle to establish the existence of pseudo-almost automorphic solutions to some second-order damped integro-differential equations…
We consider modifications of the classical dbar-Neumann conditions that define Fredholm problems for the Spin_C Dirac operator. In part II, we use boundary layer methods to obtain subelliptic estimates for these boundary value problems.…
We study the local and global well-posedness of the periodic boundary value problem for the nonlinear Schr\"odinger-Boussinesq system. The existence of periodic pulses as well as the stability of such solutions are also considered.
We study equivariant coarse homology theories through an axiomatic framework. To this end we introduce the category of equivariant bornological coarse spaces and construct the universal equivariant coarse homology theory with values in the…
The stationary, axisymmetric reduction of the vacuum Einstein equations, the so-called Ernst equation, is an integrable nonlinear PDE in two dimensions. There now exists a general method for analyzing boundary value problems for integrable…
For the self-adjoint operator of the $p$th derivative, a system of fundamental solutions is constructed. This system is analogues to the classical system of sines and cosines. The properties of such functions are studied. Classes of…
Functional determinants for Dirac operators on manifolds with boundary are considered. Ellipticity of boundary value problems is discussed in terms of the Calderon projector. The functional determinant for a Dirac operator on a…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
We introduce the concepts of branched coarse coverings and transfers between coarse homology theories along them. We show that various versions of coarse $K$-homology theories admit the additional structure of transfers. We show versions of…
A definition of invariance in Lie's sense for a boundary value problem (BVP) with the basic evolution differential equations is proposed. A problem of group classification at a wide class of BVPs parameterized by arbitrary elements is…
A variational principle is constructed for gravity coupled to an asymptotically linear dilaton and a p-form field strength. This requires the introduction of appropriate surface terms -- also known as `boundary counterterms' -- in the…
The boundary-value problem on semi-axis for one class operator-differential equations of the fourth order, the main part of which has the multiple characteristic is investigated in this paper in Sobolev type weighted space. Correctness and…
We investigate numerically the spectral flow introduced by Adams for the staggered Dirac operator on realistic (quenched) gauge configurations. We obtain clear numerical evidence that the definition works as expected: there is a clear…
Ellipticity of boundary value problems is characterized in terms of the Calderon projector. The presence of topological obstructions for the chiral Dirac operator under local boundary conditions in even dimension is discussed. Functional…