Criterion for the functional dissipativity of the Lamé operator

2021/08/13 by Cialdea, A., Maz'ya, V. · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2108.06299

Abstract

After introducing the concept of functional dissipativity of the Dirichlet problem in a domain Ω⊂ \mathbb R^N for systems of partial differential operators of the form ∂_h(\mathscr A^hk(x)∂_k) (\mathscr A^hk(x) being m × m matrices with complex valued L^∞ entries), we find necessary and sufficient conditions for the functional dissipativity of the two-dimensional Lamé 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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