Extension of the Günter derivatives to Lipschitz domains and application to the boundary potentials of elastic waves - Archive ouverte HAL Access content directly
Journal Articles Journal of Applied Mechanics and Technical Physics Year : 2020

Extension of the Günter derivatives to 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 C^2 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 of this function in the canonical orthonormal basis of the ambient space. This, in particular, implies that these derivatives define bounded operators from H^s to H^{s-1} (0 ≤ s ≤ 1) on the boundary of the Lipschitz domain and can easily be implemented in boundary element codes. Representations of the Günter operator and potentials of single and double layers of elastic waves in the two-dimensional case are provided.
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Dates and versions

hal-01395952 , version 1 (14-11-2016)
hal-01395952 , version 2 (07-07-2020)

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Abderrahmane Bendali, Sébastien Tordeux, Yuriy Matveevich Volchkov. Extension of the Günter derivatives to Lipschitz domains and application to the boundary potentials of elastic waves. Journal of Applied Mechanics and Technical Physics, 2020, 61 (1), pp.21. ⟨10.1134/S0021894420010150⟩. ⟨hal-01395952v2⟩
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