相关论文: Behaviour of the Stokes operators under domain per…
This paper investigates the stability properties of the spectrum of the classical Steklov problem under domain perturbation. We find conditions which guarantee the spectral stability and we show their optimality. We emphasize the fact that…
In the present paper we study the solvability of the Dirichlet problem for second order divergence form elliptic operators with bounded measurable coefficients which are small perturbations of given operators in rough domains beyond the…
In a bounded domain, we consider a variable range nonlocal operator, which is maximally isotropic in the sense that its radius of interaction equals the distance to the boundary. We establish $C^{1,\alpha}$ boundary regularity and existence…
A Schr\"odinger operator that is bounded below and has a unique positive ground state can be transformed into a Dirichlet form operator by the ground state transformation. If the resulting Dirichlet form operator is hypercontractive, Davies…
We study the spectrum of two kinds of operators involving a conical geometry: the Dirichlet Laplacian in conical layers and Schr\"odinger operators with attractive $\delta$-interactions supported by infinite cones. Under the assumption that…
We study the behaviour of functions of pairs of commuting self-adjoint operators under perturbations by relatively bounded operators. We obtain analogs of our earlier results for functions of a single self-adjoint operator under relatively…
We study the effect of domain perturbation on invariant manifolds for semilinear parabolic equations subject to Dirichlet boundary condition. Under Mosco convergence assumption on the domains, we prove the upper and lower semicontinuity of…
Given a Schr\"odinger operator with a real-valued potential on a bounded, convex domain or a bounded interval we prove inequalities between the eigenvalues corresponding to Neumann and Dirichlet boundary conditions, respectively. The…
The isogeometric approximation of the Stokes problem in a trimmed domain is studied. This setting is characterized by an underlying mesh unfitted with the boundary of the physical domain making the imposition of the essential boundary…
We study the boundary regularity of solutions to divergence form operators which are small perturbations of operators for which the boundary regularity of solutions is known. An operator is a small perturbation of another operator if the…
In their work on differential operators in positive characteristic, Smith and Van den Bergh define and study the derived functors of differential operators; they arise naturally as obstructions to differential operators reducing to positive…
We consider the Schrodinger operator a given domain. Our goal is to study some optimization problems where an optimal (non-negative) potential V has to be determined in some suitable admissible classes and for some suitable optimization…
We study the quasi-mode of Stokes system posed on a smooth bounded domain with Dirichlet boundary condition. We prove that the high energy L2 norm of solutions concentrate on the bi-characteristic of Laplace operator as matrix-valued Radon…
For an unbounded operator $S$ on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on $S$ is the uniform boundedness of the resolvent along…
We numerically investigate the generalized Steklov problem for the modified Helmholtz equation and focus on the relation between its spectrum and the geometric structure of the domain. We address three distinct aspects: (i) the asymptotic…
We study the strong solvability of the nonstationary Stokes problem with non-zero divergence in a bounded domain.
A framework is developed for a robust and highly accurate numerical solution of the coupled Stokes-Darcy system in three dimensions. The domain decomposition method is based on a Dirichlet-Neumann type splitting of the interface conditions…
Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This…
All the known counterexamples to Kac' famous question "can one hear the shape of a drum", i.e., does isospectrality of two Laplacians on domains imply that the domains are congruent, consist of pairs of domains composed of copies of…
We study composition operators on spaces of double Dirichlet series, focusing our interest on the characterization of the composition operators of the space of bounded double Dirichlet series $\HCdos$. We also show how the composition…