Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations

Dean Baskin; Euan A. Spence; Jared Wunsch

doi:10.1137/15M102530X

Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations

Dean Baskin, Euan A. Spence, Jared Wunsch

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Abstract

We consider three problems for the Helmholtz equation in interior and
exterior domains in R^d, (d = 2, 3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions to these problems that, in combination, give bounds on the inverses of the combined-field boundary integral operators for exterior Helmholtz problems.

Original language	English
Pages (from-to)	229-267
Journal	SIAM Journal on Mathematical Analysis (SIMA)
Volume	48
Issue number	1
DOIs	https://doi.org/10.1137/15M102530X
Publication status	Published - 2016

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10.1137/15M102530X

1504.01037v3Accepted author manuscript, 503 KB

http://dx.doi.org/10.1137/15M102530X

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title = "Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations",

abstract = "We consider three problems for the Helmholtz equation in interior andexterior domains in R^d, (d = 2, 3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions to these problems that, in combination, give bounds on the inverses of the combined-field boundary integral operators for exterior Helmholtz problems.",

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AU - Baskin, Dean

AU - Spence, Euan A.

AU - Wunsch, Jared

PY - 2016

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N2 - We consider three problems for the Helmholtz equation in interior andexterior domains in R^d, (d = 2, 3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions to these problems that, in combination, give bounds on the inverses of the combined-field boundary integral operators for exterior Helmholtz problems.

AB - We consider three problems for the Helmholtz equation in interior andexterior domains in R^d, (d = 2, 3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions to these problems that, in combination, give bounds on the inverses of the combined-field boundary integral operators for exterior Helmholtz problems.

UR - http://dx.doi.org/10.1137/15M102530X

U2 - 10.1137/15M102530X

DO - 10.1137/15M102530X

M3 - Article

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VL - 48

SP - 229

EP - 267

JO - SIAM Journal on Mathematical Analysis (SIMA)

JF - SIAM Journal on Mathematical Analysis (SIMA)

IS - 1

ER -

Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations

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Post Doc Fellowship - New Methods and Analysis for Wave Propagation Problems

Euan Spence

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Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations

Abstract

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Euan Spence

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