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arXiv · 2108.06299

Criterion for the functional dissipativity of the Lam\'e operator

A. Cialdea·V. Maz'ya
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Abstract

After introducing the concept of functional dissipativity of the Dirichlet problem in a domain $\Omega\subset {\mathbb R}^N$ for systems of partial differential operators of the form $\partial_{h}({\mathscr A}^{hk}(x)\partial_{k})$ (${\mathscr A}^{hk}(x)$ being $m \times m$ matrices with complex valued $L^\infty$ entries), we find necessary and sufficient conditions for the functional dissipativity of the two-dimensional Lam\'e system. As an application of our theory we provide two regularity results for the displacement vector in the $N$-dimensional equilibrium problem, when the body is fixed along its boundary.

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A. Cialdea, V. Maz'ya. 2021-08-13. Criterion for the functional dissipativity of the Lam\'e operator. https://arxiv.org/abs/2108.06299

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