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Extension of the Günter Derivatives to the Lipschitz Domains and Application to the Boundary Potentials of Elastic Waves. / Bendali, A.; Tordeux, S.; Volchkov, Yu M.

In: Journal of Applied Mechanics and Technical Physics, Vol. 61, No. 1, 01.01.2020, p. 139-156.

Research output: Contribution to journal › Article › peer-review

Harvard

Bendali, A, Tordeux, S & Volchkov, YM 2020, 'Extension of the Günter Derivatives to the Lipschitz Domains and Application to the Boundary Potentials of Elastic Waves', Journal of Applied Mechanics and Technical Physics, vol. 61, no. 1, pp. 139-156. https://doi.org/10.1134/S0021894420010150

APA

Bendali, A., Tordeux, S., & Volchkov, Y. M. (2020). Extension of the Günter Derivatives to the Lipschitz Domains and Application to the Boundary Potentials of Elastic Waves. Journal of Applied Mechanics and Technical Physics, 61(1), 139-156. https://doi.org/10.1134/S0021894420010150

Vancouver

Bendali A, Tordeux S, Volchkov YM. Extension of the Günter Derivatives to the Lipschitz Domains and Application to the Boundary Potentials of Elastic Waves. Journal of Applied Mechanics and Technical Physics. 2020 Jan 1;61(1):139-156. doi: 10.1134/S0021894420010150

Author

Bendali, A. ; Tordeux, S. ; Volchkov, Yu M. / Extension of the Günter Derivatives to the Lipschitz Domains and Application to the Boundary Potentials of Elastic Waves. In: Journal of Applied Mechanics and Technical Physics. 2020 ; Vol. 61, No. 1. pp. 139-156.

BibTeX

@article{8c63cd31f7694983bfef5677bbbdbbd4,
title = "Extension of the G{\"u}nter Derivatives to the Lipschitz Domains and Application to the Boundary Potentials of Elastic Waves",
abstract = "Regularization techniques for the trace and the traction of elastic waves potentials previously built for domains of the class C2 are extended to the Lipschitz case. In particular, this yields an elementary way to establish the mapping properties of elastic wave potentials from those of the scalar Helmholtz equation without resorting to the more advanced theory for elliptic systems in the Lipschitz domains. Scalar G{\"u}nter derivatives of a function defined on the boundary of a three-dimensional domain are expressed as components (or their opposites) of the tangential vector rotational ∇∂Ωu × n of this function in the canonical orthonormal basis of the ambient space. This, in particular, implies that these derivatives define bounded operators from Hs to Hs−1 (0 ≤ s ≤ 1) on the boundary of the Lipschitz domain and can easily be implemented in boundary element codes. Representations of the Gu{\"u}nter operator and potentials of single and double layers of elastic waves in the two-dimensional case are provided.",
keywords = "boundary integral operators, elastic waves, G{\"u}nter derivatives, layer potentials, Lipschitz domains, Gunter derivatives, INTEGRAL-EQUATIONS, MAXWELL, FORMULATION, RADIATION, SCATTERING",
author = "A. Bendali and S. Tordeux and Volchkov, {Yu M.}",
year = "2020",
month = jan,
day = "1",
doi = "10.1134/S0021894420010150",
language = "English",
volume = "61",
pages = "139--156",
journal = "Journal of Applied Mechanics and Technical Physics",
issn = "0021-8944",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "1",

}

RIS

TY - JOUR

T1 - Extension of the Günter Derivatives to the Lipschitz Domains and Application to the Boundary Potentials of Elastic Waves

AU - Bendali, A.

AU - Tordeux, S.

AU - Volchkov, Yu M.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - Regularization techniques for the trace and the traction of elastic waves potentials previously built for domains of the class C2 are extended to the Lipschitz case. In particular, this yields an elementary way to establish the mapping properties of elastic wave potentials from those of the scalar Helmholtz equation without resorting to the more advanced theory for elliptic systems in the Lipschitz domains. Scalar Günter derivatives of a function defined on the boundary of a three-dimensional domain are expressed as components (or their opposites) of the tangential vector rotational ∇∂Ωu × n of this function in the canonical orthonormal basis of the ambient space. This, in particular, implies that these derivatives define bounded operators from Hs to Hs−1 (0 ≤ s ≤ 1) on the boundary of the Lipschitz domain and can easily be implemented in boundary element codes. Representations of the Guünter operator and potentials of single and double layers of elastic waves in the two-dimensional case are provided.

AB - Regularization techniques for the trace and the traction of elastic waves potentials previously built for domains of the class C2 are extended to the Lipschitz case. In particular, this yields an elementary way to establish the mapping properties of elastic wave potentials from those of the scalar Helmholtz equation without resorting to the more advanced theory for elliptic systems in the Lipschitz domains. Scalar Günter derivatives of a function defined on the boundary of a three-dimensional domain are expressed as components (or their opposites) of the tangential vector rotational ∇∂Ωu × n of this function in the canonical orthonormal basis of the ambient space. This, in particular, implies that these derivatives define bounded operators from Hs to Hs−1 (0 ≤ s ≤ 1) on the boundary of the Lipschitz domain and can easily be implemented in boundary element codes. Representations of the Guünter operator and potentials of single and double layers of elastic waves in the two-dimensional case are provided.

KW - boundary integral operators

KW - elastic waves

KW - Günter derivatives

KW - layer potentials

KW - Lipschitz domains

KW - Gunter derivatives

KW - INTEGRAL-EQUATIONS

KW - MAXWELL

KW - FORMULATION

KW - RADIATION

KW - SCATTERING

UR - http://www.scopus.com/inward/record.url?scp=85088919557&partnerID=8YFLogxK

U2 - 10.1134/S0021894420010150

DO - 10.1134/S0021894420010150

M3 - Article

AN - SCOPUS:85088919557

VL - 61

SP - 139

EP - 156

JO - Journal of Applied Mechanics and Technical Physics

JF - Journal of Applied Mechanics and Technical Physics

SN - 0021-8944

IS - 1

ER -

ID: 24957451