A nonlinear Korn inequality on a surface with an explicit estimate of the constant
Maria Mălin, Cristinel Mardare · 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 < p < ∞ . We establish a new inequality of this type. The novelty is that the immersion θ belongs to a specific set of mappings of class 𝒞 1 from ω ¯ into ℝ 3 with a unit vector field also of class 𝒞 1 over ω ¯ .