Related papers: Trace expansions for elliptic cone operators with …
We give a simple, explicit, sufficient condition for the existence of a sector of minimal growth for second order regular singular differential operators on graphs. We specifically consider operators with a singular potential of Coulomb…
We study operators on a singular manifold, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. The idea is to construct so-called…
We investigate minimal operator corresponding to operator differential expression with exit from space, study its selfadjoint extensions, also for one particular selfadjoint extension corresponding to boundary value problem with some…
We shall investigate the asymptotic behavior of the extended resolvent R(s) of the Dirac operator as |s| increases to infinity, where s is a real parameter. It will be shown that the norm of R(s), as a bounded operator between two weighted…
We use the boundary triplet approach to extend the classical concept of perturbation determinants to a more general setup. In particular, we examine the concept of perturbation determinants to pairs of proper extensions of closed symmetric…
We study asymptotic behaviors of solutions to the Loewner-Nirenberg problem in finite cones and establish optimal asymptotic expansions in terms of the corresponding solutions in infinite cones. The spherical domains over which cones are…
We analyze the asymptotic behavior of eigenvalues and eigenfunctions of an elliptic operator with mixed boundary conditions on cylindrical domains when the length of the cylinder goes to infinity. We identify the correct limiting problem…
The aim of this work is to characterize the asymptotic behaviour of the first eigenfunction of the generalised p-Laplace operator with mixed (Dirichlet and Neumann) boundary conditions in cylindrical domains when the length of the…
The purpose of this paper is to present the construction of a canonical determinant functional on elliptic pseudodifferential operators associated to the Guillemin-Wodzicki residue trace. The resulting functional is multiplicative, a local…
We obtain a unique continuation result at infinity for fully nonlinear elliptic integro-differential operators of order 2s which satisfy the maximum and minimum principles in bounded subdomains, under the decay assumption $o(|x|^{-(N+2s)})$…
We develop a discrete extension operator for trimmed spline spaces consisting of piecewise polynomial functions of degree $p$ with $k$ continuous derivatives. The construction is based on polynomial extension from neighboring elements…
We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected…
This is a survey of recent results on zeta- and eta-function poles and values for realizations of Laplace- and Dirac-type operators defined by pseudodifferential projection boundary conditions (including the Atiyah-Patodi-Singer operator…
We give a uniform description of resolvents and complex powers of elliptic semiclassical cone differential operators as the semiclassical parameter $h$ tends to $0$. An example of such an operator is the shifted semiclassical Laplacian…
Depending of the geometry of the domain, one can define --at least-- three different Stokes operators with Dirichlet boundary conditions. We describe how the resolvents of these Stokes operators converge with respect to a converging…
We study the adjointness problem for the closed extensions of a general b-elliptic operator A in x^{-\nu}Diff^m_b(M;E), \nu>0, initially defined as an unbounded operator A:C_c^\infty(M;E)\subset x^\mu L^2_b(M;E)\to x^\mu L^2_b(M;E), \mu \in…
We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense…
A new pseudodifferential calculus of Shubin type is introduced. The calculus contains operators depending on a non negative real parameter as well as operators independent of the parameter. Resolvents of Shubin type pseudodifferential…
We consider a non-uniformly elliptic second-order differential operator with periodic coefficients that models composite media consisting of highly anisotropic cylindrical fibres periodically distributed in an isotropic background. The…
In this note self-adjoint realizations of second order elliptic differential expressions with non-local Robin boundary conditions on a domain $\Omega\subset\dR^n$ with smooth compact boundary are studied. A Schatten--von Neumann type…