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In this note we discuss the (higher) regularity properties of the Signorini problem for the homogeneous, isotropic Lame system. Relying on an observation by Schumann cite{Schumann1}, we reduce the question of the solutions and the free boundary regularity for the homogeneous, isotropic Lame system to the corresponding regularity properties of the obstacle problem for the half-Laplacian.
We investigate the regularity of the free boundary for the Signorini problem in $mathbb{R}^{n+1}$. It is known that regular points are $(n-1)$-dimensional and $C^infty$. However, even for $C^infty$ obstacles $varphi$, the set of non-regular (or degen
We prove a higher regularity result for the free boundary in the obstacle problem for the fractional Laplacian via a higher order boundary Harnack inequality.
For two neighbouring stiff inclusions, the stress, which is the gradient of a solution to the Lam{e} system of linear elasticity, may exhibit singular behavior as the distance between these two inclusions becomes arbitrarily small. In this paper, a f
In this note, we use an epiperimetric inequality approach to study the regularity of the free boundary for the parabolic Signorini problem. We show that if the vanishing order of a solution at a free boundary point is close to $3/2$ or an even intege
In this paper we prove a quantitative form of the strong unique continuation property for the Lame system when the Lame coefficients $mu$ is Lipschitz and $lambda$ is essentially bounded in dimension $nge 2$. This result is an improvement of our earl