The forward problem for the electromagnetic Helmholtz equation with critical singularities
From MaRDI portal
Publication:390752
DOI10.1016/j.aim.2013.03.012zbMath1284.35144arXiv1211.1030OpenAlexW2009844386MaRDI QIDQ390752
Luis Vega, Miren Zubeldia, Juan Antonio Barceló
Publication date: 8 January 2014
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1211.1030
PDEs in connection with optics and electromagnetic theory (35Q60) Singular perturbations in context of PDEs (35B25) Scattering theory for PDEs (35P25) Spectrum, resolvent (47A10) A priori estimates in context of PDEs (35B45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)
Related Items
A limiting absorption principle for the Helmholtz equation with variable coefficients ⋮ Resolvent and Strichartz estimates for elastic wave equations ⋮ Global Strichartz estimates for an inhomogeneous Maxwell system ⋮ Absence of eigenvalues of two-dimensional magnetic Schrödinger operators ⋮ Uniform resolvent and Strichartz estimates for Schrödinger equations with critical singularities ⋮ Global-in-time smoothing effects for Schrödinger equations with inverse-square potentials ⋮ Eigenvalue bounds for non-self-adjoint Schrödinger operators with the inverse-square potential ⋮ Uniform Sobolev estimates for Schrödinger operators with scaling-critical potentials and applications ⋮ Uniform resolvent estimates and absence of eigenvalues for Lamé operators with complex potentials ⋮ Remarks on endpoint Strichartz estimates for Schrödinger equations with the critical inverse-square potential ⋮ Unique continuation for the magnetic Schrödinger operator with singular potentials
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Time decay of scaling critical electromagnetic Schrödinger flows
- Spectral representations for Schrödinger operators with long-range potentials
- Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential
- Eikonal equations and spectral representations for long-range Schrödinger Hamiltonians
- Endpoint Strichartz estimates for the magnetic Schrödinger equation
- Magnetic virial identities, weak dispersion and Strichartz inequalities
- Non-trapping magnetic fields and Morrey-Campanato estimates for Schrödinger operators
- Spectral representation for Schrödinger operators with magnetic vector potentials
- Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators
- Schrödinger operators with a nonspherical radiation condition
- Asymptotic properties of solutions of differential equations with simple characteristics
- On the asymptotic behavior of the solutions of the Schrödinger equation \((-\Delta+Q(y)-k^2V=F)\)
- Eigenfunction expansions for the Schrödinger operators with longrange potentials \(Q(y)=O(| y|^{-\varepsilon}),\;\varepsilon >0\)
- Scattering theory for Schrödinger operators with long-range potentials. I. Abstract theory
- Scattering theory for Schrödinger operators with long-range potentials. II: Spectral and scattering theory
- Morrey-Campanato estimates for Helmholtz equations
- Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential
- Energy concentration and explicit Sommerfeld radiation condition for the electromagnetic Helmholtz equation
- Local regularity of solutions to wave equations with time-dependent potentials
- Multipliers and Morrey spaces
- Relativistic Hardy inequalities in magnetic fields
- Strichartz and smoothing estimates for Schrödinger operators with large magnetic potentials in \(\mathbb R^3\)
- Some dispersive estimates for Schrödinger equations with repulsive potentials
- Spherical perturbations of Schrödinger equations
- Effective limiting absorption principles, and applications
- Scattering theory for differential operators. I: Operator theory
- Scattering theory for differential operators. II: Self-adjoint elliptic operators
- Limiting absorption method and absolute continuity for the Schrödinger operator
- COUNTEREXAMPLES TO STRICHARTZ ESTIMATES FOR THE MAGNETIC SCHRÖDINGER EQUATION
- On the existence and the unitary property of the scattering operator
- Weak Dispersive Estimates for Schrödinger Equations with Long Range Potentials
- Decay estimates for Schrödinger operators
- SOME EXAMPLES OF SMOOTH OPERATORS AND THE ASSOCIATED SMOOTHING EFFECT
- Some special solutions of the Schr\"odinger equation
- Counterexamples of Strichartz inequalities for Schrodinger equations with repulsive potentials
- Time decay for the nonlinear Klein-Gordon equation
- Schrödinger operators with singular magnetic vector potentials
This page was built for publication: The forward problem for the electromagnetic Helmholtz equation with critical singularities
