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

Giulio Starita and Alfonsina Tartaglione
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Giulio Starita: Department of Mathematics and Physics, University of Campania, 81100 Caserta, Italy
Alfonsina Tartaglione: Department of Mathematics and Physics, University of Campania, 81100 Caserta, Italy

Mathematics, 2019, vol. 7, issue 2, 1-12

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.

Keywords: linear elastostatics; layer potentials; fredholmian operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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