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\(W^{2,p}\) regularity of the displacement problem for the Lamé system on \(W^{2,s}\) domains. (English) Zbl 0934.35041

Summary: On certain bounded \(C^1\) domains \(\Omega\) that are not necessarily \(C^{1,1}\), we prove that the Dirichlet problem \(Lu=f\) on \(\Omega\), \(u=0\) on \(\partial\Omega\) with \(f\in L^p(\Omega)\) is well posed in \(W^{2,p} (\Omega) \cap W^{1,p}_0 (\Omega)\) for all \(p\in(1,+ \infty)\), where \(L\) is the three-dimensional Lamé system in linear elasticity.

MSC:

35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
74B05 Classical linear elasticity
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