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Mathematics 2019, 7(2), 134; https://doi.org/10.3390/math7020134

On the Fredholm Property of the Trace Operators Associated with the Elastic Layer Potentials

Department of Mathematics and Physics, University of Campania, 81100 Caserta, Italy
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Received: 21 December 2018 / Revised: 22 January 2019 / Accepted: 24 January 2019 / Published: 1 February 2019
(This article belongs to the Special Issue Advanced Mathematical Methods: Theory and Applications)
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Abstract

We deal with the system of equations of linear elastostatics, governing the equilibrium configurations of a linearly elastic body. We recall the basics of the theory of the elastic layer potentials and we extend the trace operators associated with the layer potentials to suitable sets of singular densities. We prove that the trace operators defined, for example, on W 1 k 1 / q , q ( Ω ) (with k 2 , q ( 1 , + ) and Ω an open connected set of R 3 of class C k ), satisfy the Fredholm property. View Full-Text
Keywords: linear elastostatics; layer potentials; fredholmian operators linear elastostatics; layer potentials; fredholmian operators
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Starita, G.; Tartaglione, A. On the Fredholm Property of the Trace Operators Associated with the Elastic Layer Potentials. Mathematics 2019, 7, 134.

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