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The sharp Korn interpolation and second inequalities in thin domains
Davit Harutyunyan
In the present paper we extend the Korn interpolation and second inequalities in thin domains, proven in [\ref{bib:Harutyunyan.4}], to the space for any A…
A note on the extreme points of the cone of quasiconvex quadratic forms with orthotropic symmetry
Davit Harutyunyan
We study the extreme points of the cone of quasiconvex quadratic forms with linear elastic orthotropic symmetry. We prove that if the determinant of the acoustic matrix of the asso…
The asymptotically sharp Korn interpolation and second inequalities for shells
Davit Harutyunyan
We consider shells in three dimensional Euclidean space which have bounded principal curvatures. We prove Korn's interpolation (or the so called first and a half\footnote{The inequ…
Weighted asymptotic Korn and interpolation Korn inequalities with singular weights
Davit Harutyunyan, Hayk Mikayelyan
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…
On the maximization of the solution of Poisson's equation: Brezis-Gallouet-Wainger type inequalities and applications
Davit Harutyunyan, Hayk Mikayelyan
For the solution of the Poisson problem with an right hand side \begin{equation*} \begin{cases} -Δu(x) = f (x) & \mbox{in } D, u=0 & \mbox{on } \partial D, \end{cases} \…
Korn inequalities for shells with zero Gaussian curvature
Yury Grabovsky, Davit Harutyunyan
We consider shells with zero Gaussian curvature, namely shells with one principal curvature zero and the other one having a constant sign. Our particular interests are shells that…