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Completeness Theorems on the Boundary in Thermoelasticity

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Analysis as a Life

Part of the book series: Trends in Mathematics ((TM))

Abstract

The steady oscillation equations of thermoelasticity theory are considered and the completeness (in the sense of Picone) on the boundary of a given bounded domain of the class of exponential polynomial solutions is proved. In the particular case of the equations of thermoelasto-static state we establish the completeness of the polynomial solutions.

To Prof. Heinrich Begehr on occasion of his 80th birthday

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Notes

  1. 1.

    The Gårding inequality which is equivalent to ellipticity is the following

  2. 2.

    By a regular solution we mean a vector to which one can apply Green formulas. For example, a simple layer potential with densities in L p( Σ) is regular in this sense.

  3. 3.

    This and the other BVPs are considered in the spaces of vectors which can be represented as simple layer potentials with L p densities. See [24] for more details.

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Authors and Affiliations

  1. Department of Mathematics, Computer Science and Economics, University of Basilicata, Potenza, Italy

    Alberto Cialdea

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  1. Alberto Cialdea
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Correspondence to Alberto Cialdea .

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Editors and Affiliations

  1. Department of Economics, Belarusian State University, Minsk, Belarus

    Sergei Rogosin

  2. Mathematics Department, Yeditepe University, Ataşehir, Istanbul, Turkey

    Ahmet Okay Çelebi

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Cialdea, A. (2019). Completeness Theorems on the Boundary in Thermoelasticity. In: Rogosin, S., Çelebi, A. (eds) Analysis as a Life. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-02650-9_6

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