Weighted asymptotic Korn and interpolation Korn inequalities with singular weights

Harutyunyan, Davit; Mikayelyan, Hayk

doi:10.1090/proc/14533

Weighted asymptotic Korn and interpolation Korn inequalities with singular weights
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by Davit Harutyunyan and Hayk Mikayelyan PDF

Proc. Amer. Math. Soc. 147 (2019), 3635-3647 Request permission

Abstract:

In this work we derive asymptotically sharp weighted Korn and Korn-like interpolation (or first and a half) inequalities in thin domains with singular weights. The constants $K$ (Korn’s constant) in the inequalities depend on the domain thickness $h$ according to a power rule $K=Ch^\alpha ,$ where $C>0$ and $\alpha \in R$ are constants independent of $h$ and the displacement field. The sharpness of the estimates is understood in the sense that the asymptotics $h^\alpha$ is optimal as $h\to 0.$ The choice of the weights is motivated by several factors; in particular a spatial case occurs when making Cartesian to polar change of variables in two dimensions.

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