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

Extension of the Günter Derivatives to the Lipschitz Domains and Application to the Boundary Potentials of Elastic Waves Full article

Journal

Journal of Applied Mechanics and Technical Physics
ISSN: 0021-8944

Output data

Year: 2020, Volume: 61, Number: 1, Pages: 139-156 Pages count : 18 DOI: 10.1134/s0021894420010150

Tags

boundary integral operators, Günter derivatives, elastic waves, layer potentials, Lipschitz domains

Authors

Bendali Abderrahmane ¹ , Tordeux Sébastien ² , Volchkov Yuriy ³

Affiliations

1	Institut Mathématique de Toulouse, Université de Toulouse, Toulouse, France
2	Université de Pau et des Pays de l’Adour, Pau, France
3	Lavrent’ev Institute for Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

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.

Bendali A. , Tordeux S. , Volchkov Y.
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. V.61. N1. P.139-156. DOI: 10.1134/s0021894420010150 WOS Scopus РИНЦ OpenAlex

Submitted:	Jul 10, 2019
Accepted:	Jul 29, 2019
Published print:	Aug 5, 2020

Web of science:	WOS:000556247100015
Scopus:	2-s2.0-85088919557
Elibrary:	45416192
OpenAlex:	W3043856755

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