Related papers: Parameter-dependent Edge Operators
Given a pair of smooth transversally intersecting manifolds in some ambient manifold, we construct an operator algebra generated by pseudodifferential operators and the (co)boundary operators associated with the submanifolds. We show that…
We give a systematic and self-contained account of the construction of geometrically decomposed bases and degrees of freedom in finite element exterior calculus. In particular, we elaborate upon a previously overlooked basis for one of the…
We obtain sharp uniform bounds on the low lying eigenfunctions for a class of semiclassical pseudodifferential operators with double characteristics and complex valued symbols, under the assumption that the quadratic approximations along…
We expand on some invariants used for classifying nonselfadjoint operator algebras. Specifically to nonselfadjoint operator algebras which have a conditional expectation onto a commutative diagonal we construct an edge-colored directed…
We consider divergence form operators with complex coefficients on an open subset of Euclidean space. Boundary conditions in the corresponding parabolic problem are dynamical, that is, the time derivative appears on the boundary. As a…
In this paper operator pencils $A(x,D,\lambda)$ are studied which act on a manifold with boundary and satisfy the condition of $N$-ellipticity with parameter, a generalization of the notion of ellipticity with parameter as introduced by…
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
Motivated by the study of layer potentials on manifolds with straight conical or cylindrical ends, we introduce and study two classes (or calculi) of pseudodifferential operators defined on manifolds with cylindrical ends: the class of…
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…
We prove the validity of maximum principles for a class of fully nonlinear operators on unbounded subdomains $\Omega \subset \mathbb R^n$ of cylindrical type. The main structural assumption is the uniform ellipticity of the operator along…
In this paper we study the shape differentiability properties of a class of boundary integral operators and of potentials with weakly singular pseudo-homogeneous kernels acting between classical Sobolev spaces, with respect to smooth…
We study Laplace-type operators on hybrid manifolds, i.e. on configurations consisting of closed two-dimensional manifolds and one-dimensional segments. Such an operator can be constructed by using the Laplace-Beltrami operators on each…
We study the topological configurations of the lines of principal curvature, the asymptotic and characteristic curves on a cuspidal edge, in the domain of a parametrization of this surface as well as on the surface itself. Such…
We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifold with corners of in general higher codimension, and we…
We develop a theoretical framework for computer-assisted proofs of the existence of invariant objects in semilinear PDEs. The invariant objects considered in this paper are equilibrium points, traveling waves, periodic orbits and invariant…
We consider special elliptic operators in functional spaces on manifolds with a boundary which has some singular points. Such an operator can be represented by a sum of operators, and for a Fredholm property of an initial operator one needs…
We give embedding theorems for weighted Bergman-Orlicz spaces on the ball and then apply our results to the study of composition operators in this context. As one of the motivations of this work, we show that there exist some weighted…
Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds…
We prove the boundedness on $L^p$, $1<p<\infty$, of operators on manifolds which arise by taking conditional expectation of transformations of stochastic integrals. These operators include various classical operators such as second order…
In this survey paper we present a class of shape optimization problems where the cost function involves the solution of a PDE of elliptic type in the unknown domain. In particular, we consider cost functions which depend on the spectrum of…