Strong unique continuation and global regularity estimates for nanoplates

2022/09/19 by Antonino Morassi, Morassi, Antonino, Edi Rosset +5
Computer Science · Engineering · Materials Science · #35B60 #35J30 #74K20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Nonlocal and gradient elasticity in micro/nano structures

paper · pdf · doi:10.48550/arxiv.2209.08830

openalex publication_date 2022/09/19 · openalex created_date 2022/09/21 · openalex updated_date 2026/07/28

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.

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