3 problems

Conjecture on Grad's number. As the domain $\Omega$ approaches axial symmetry, Grad's number tends to zero:

Desvillettes–Villani conjecture. Grad's number $c_{\mathsf{g}}=c_{\mathsf{g}}(\Omega)$ steers the blow-up of the first Korn constant $c_{\mathsf{k,n}}$ as $\Omega$ approaches axial…

Boundary Korn inequality. There exists a positive constant $\tilde{K}$ such that, for every $\mathbf{u}\in\mathbf{H}^2(\Omega)$,