A priori bounds for solutions of the Dirichlet problem for [Delta + lambda sup(2) n(x)]u = f(x,lambda) on an exterior domain

DOI10.1016/0022-0396(77)90011-0zbMath0353.35031OpenAlexW2054066080WikidataQ125855514 ScholiaQ125855514MaRDI QIDQ1236268

Clifford O. Bloom, Nicholas D. Kazarinoff

Publication date: 1977

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(77)90011-0

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) A priori estimates in context of PDEs (35B45) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

Scattering by Finely Layered Obstacles: Frequency-Explicit Bounds and Homogenization ⋮ Explicit bounds for the high-frequency time-harmonic Maxwell equations in heterogeneous media ⋮ The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances ⋮ Acoustic transmission problems: Wavenumber-explicit bounds and resonance-free regions ⋮ Numerical Computation of Waves at High Frequencies by an Iterated WKB‐Method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local energy decay for a class of nonstar-shaped bodies
• A rate of approach to the steady state of solutions of second-order hyperbolic equations
• Estimates for solutions of reduced hyperbolic equations to the second order with a large parameter
• Dispersal of waves vanishing on the boundary of an exterior domain
• Decay for solutions of the exterior problem for the wave equation
• High‐frequency scattering by finite convex regions
• The geometry of immersions. II
• An inequality for the reduced wave operator and the justification of geometrical optics
• Solutions of the wave equation with localized energy