Generalized Robin Boundary Conditions, Robin-to-Dirichlet Maps, and Krein-Type Resolvent Formulas for Schr\"odinger Operators on Bounded Lipschitz Domains
From MaRDI portal
Publication:5506168
zbMath1178.35147arXiv0803.3179MaRDI QIDQ5506168
Marius Mitrea, Friedrich Gesztesy
Publication date: 28 January 2009
Full work available at URL: https://arxiv.org/abs/0803.3179
bounded Lipschitz domainsKrein type formulasMulti-dimensional Schrödinger operatorsRobin-to-Dirichlet and Dirichlet-to-Neumann maps
Boundary value problems for second-order elliptic equations (35J25) General topics in linear spectral theory for PDEs (35P05) General theory of partial differential operators (47F05) Schrödinger operator, Schrödinger equation (35J10) Green's functions for elliptic equations (35J08)
Related Items
All self-adjoint extensions of the magnetic Laplacian in nonsmooth domains and gauge transformations, Scattering matrices and Dirichlet-to-Neumann maps, Generalized \(Q\)-functions and Dirichlet-to-Neumann maps for elliptic differential operators, Dirichlet-to-Neumann maps, abstract Weyl-Titchmarsh \(M\)-functions, and a generalized index of unbounded meromorphic operator-valued functions, The Maslov and Morse indices for Schrödinger operators on \([0,1\)], Spectral theory for perturbed Krein Laplacians in nonsmooth domains, Radiation conditions and integral representations for Clifford algebra-valued null-solutions of the Helmholtz operator, The proper dissipative extensions of a dual pair, Spectral enclosures for non-self-adjoint extensions of symmetric operators, Operator splitting for abstract Cauchy problems with dynamical boundary conditions, Spectral shift functions and Dirichlet-to-Neumann maps, Hadamard-type formulas via the Maslov form, The Morse and Maslov indices for Schrödinger operators, Ultracontractivity and eigenvalues: Weyl's law for the Dirichlet-to-Neumann operator, Elliptic problems with rough boundary data in generalized Sobolev spaces, Elliptic boundary value problems with \(\lambda \)-dependent boundary conditions, The Bi-Laplacian with Wentzell boundary conditions on Lipschitz domains, Spectral analysis of selfadjoint elliptic differential operators, Dirichlet-to-Neumann maps, and abstract Weyl functions, Spectral estimates for resolvent differences of self-adjoint elliptic operators, Schrödinger operators with \(\delta\) and \(\delta^{\prime}\)-potentials supported on hypersurfaces, Linear Operators and Operator Functions Associated with Spectral Boundary Value Problems, Elliptic differential operators on Lipschitz domains and abstract boundary value problems, The Maslov and Morse indices for system Schroedinger operators on \mathBB{R}, Kreĭn-like extensions and the lower boundedness problem for elliptic operators, The Dirichlet-to-Neumann operator via hidden compactness, Strict inequality of Robin eigenvalues for elliptic differential operators on Lipschitz domains, The Dirichlet-to-Neumann operator on exterior domains, Dirichlet-to-Neumann maps on bounded Lipschitz domains, The Maslov index and the spectra of second order elliptic operators, The Dirichlet-to-Neumann map for Schrödinger operators with complex potentials, Extension theory and Kreĭn-type resolvent formulas for nonsmooth boundary value problems, Spectral theory of elliptic operators in exterior domains, A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains, Boundary pairs associated with quadratic forms, On the nature of the Laplace-Beltrami operator on Lipschitz manifolds, Hodge decompositions with mixed boundary conditions and applications to partial differential equations on Lipschitz manifolds, The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates, A Survey on the Krein–von Neumann Extension, the Corresponding Abstract Buckling Problem, and Weyl-type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains, Isoparametric finite element analysis of a generalized Robin boundary value problem on curved domains, A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains, On absence of bound states for weakly attractive δ′-interactions supported on non-closed curves in ℝ2, A note on an operator-theoretic approach to classic boundary value problems for harmonic and analytic functions in complex plane domains, Inverse problems with partial data for elliptic operators on unbounded Lipschitz domains, The Morse and Maslov indices for multidimensional Schrödinger operators with matrix-valued potentials, Compactness, or lack thereof, for the harmonic double layer, Dimension Bounds in Monotonicity Methods for the Helmholtz Equation, On the eigenvalues of the Robin Laplacian with a complex parameter, Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities, Transmission boundary problems for Dirac operators on Lipschitz domains and applications to Maxwell’s and Helmholtz’s equations, Jordan chains of elliptic partial differential operators and Dirichlet-to-Neumann maps