Strong unique continuation and global regularity estimates for nanoplates
Analysis of PDEs
2023-03-13 v2
Abstract
In this paper we analyze some properties of a sixth order elliptic operator arising in the framework of the strain gradient linear elasticity theory for nanoplates in flexural deformation. We first rigorously deduce the weak formulation of the underlying Neumann problem as well as its well posedness. Under some suitable smoothness assumptions on the coefficients and on the geometry we derive interior and boundary regularity estimates for the solution of the Neumann problem. Finally, for the case of isotropic materials, we obtain new Strong Unique Continuation results in the interior, in the form of doubling inequality and three spheres inequality, by a Carlemann estimates approach.
Keywords
Cite
@article{arxiv.2209.08830,
title = {Strong unique continuation and global regularity estimates for nanoplates},
author = {Antonino Morassi and Edi Rosset and Eva Sincich and Sergio Vessella},
journal= {arXiv preprint arXiv:2209.08830},
year = {2023}
}