Weighted asymptotic korn and interpolation korn inequalities with singular weights

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 = Chα, 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 hα is optimal as h → 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.