A nonlinear Korn inequality on a surface with an explicit estimate of the constant - Malin, Maria; Mardare, Cristinel (Comptes Rendus. Mathématique, 2021)
A nonlinear Korn inequality on a surface estimates a distance between a surface $θ (ω )$ and another surface $φ (ω )$ in terms of distances between their fundamental forms in the space $L^p(ω )$, $1.We establish a new inequality of this type. The novelty is that the immersion $θ $ belongs to a specific set of mappings of class $\mathcal{C}^1$ from $\overline{ω }$ into $\mathbb{R}^3$ with a unit vector field also of class $\mathcal{C}^1$ over $\overline{ω }$.