Weighted asymptotic Korn and interpolation Korn inequalities with singular weights

2017/09/15 by Harutyunyan, Davit, Mikayelyan, Hayk
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.05040

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^α, where C>0 and α∈ R are constants independent of h and the displacement field. The sharpness of the estimates is understood in the sense that the asymptotics h^α is optimal as h→ 0. The choice of the weights is motivated by several factors, in particular a spacial case occurs when making Cartesian to polar change of variables in two dimensions.

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