The Stokes paradox in inhomogeneous elastostatics

2018/05/03 by Ferone, Adele, Russo, Remigio, Tartaglione, Alfonsina
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.01232

Abstract

We prove that the displacement problem of inhomogeneous elastostatics in a two--dimensional exterior Lipschitz domain has a unique solution with finite Dirichlet integral \u, vanishing uniformly at infinity if and only if the boundary datum satisfies a suitable compatibility condition (Stokes' paradox). Moreover, we prove that it is unique under the sharp condition \u=o(log r) and decays uniformly at infinity with a rate depending on the elasticities. In particular, if these last ones tend to a homogeneous state at large distance, then \u=O(r^-α), for every α<1.

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