A uniform resolvent estimate for a Helmholtz equation with some large perturbations in an exterior domain

DOI10.1007/978-3-030-87502-2_63MaRDI QIDQ6196723

Hideo Nakazawa

Publication date: 15 March 2024

Published in: Trends in Mathematics (Search for Journal in Brave)

zbMATH Keywords

Helmholtz equationenergy-dependent potentialdissipative wave equationlarge perturbationuniform resolvent estimate

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Scattering theory of linear operators (47A40) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Cites Work

• Uniform resolvent estimates for magnetic Schrödinger operators and smoothing effects for related evolution equations
• Smooth perturbations of the self-adjoint operator \(|\Delta|^{\alpha{}/2}\)
• Scattering theory for wave equations with dissipative terms
• Uniform resolvent estimates for magnetic Schrödinger operators in a 2D exterior domain and their applications to related evolution equations
• On the principle of limiting amplitude for dissipative wave equations
• Energy decay and asymptotic behavior of solutions to the wave equations with linear dissipation
• Uniform Resolvent Estimates for Stationary Dissipative Wave Equations in an Exterior Domain and Their Application to the Principle of Limiting Amplitude
• SOME EXAMPLES OF SMOOTH OPERATORS AND THE ASSOCIATED SMOOTHING EFFECT
• The principle of limiting absorption for the non-selfadjoint Schrödinger operator with energy dependent potential

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