A generalized Korn inequality and strong unique continuation for the Reissner-Mindlin plate system

TL;DR

This paper establishes a generalized Korn inequality and strong unique continuation properties for the Reissner-Mindlin plate system, providing new quantitative stability estimates and regularity results for elastic plates made of anisotropic and isotropic materials.

Contribution

It introduces a generalized Korn inequality applicable to anisotropic plates and derives a three spheres inequality with optimal exponent for isotropic cases, advancing the mathematical understanding of plate models.

Findings

Generalized Korn inequality for anisotropic plates

Quantitative stability and H^2 regularity for Neumann problem

Interior three spheres inequality with optimal exponent

Abstract

We prove constructive estimates for elastic plates modelled by the Reissner-Mindlin theory and made by general anisotropic material. Namely, we obtain a generalized Korn inequality which allows to derive quantitative stability and global H^2 regularity for the Neumann problem. Moreover, in case of isotropic material, we derive an interior three spheres inequality with optimal exponent from which the strong unique continuation property follows.