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.
The Gårding inequality which is equivalent to ellipticity is the following
- 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.
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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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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