Size estimates for nanoplates

Abstract

We consider the problem of determining, within an elastic isotropic nanoplate in bending, the possible presence of an inclusion made of different elastic material. Under suitable a priori assumptions on the unknown inclusion, we provide quantitative upper and lower estimates for the area of the unknown defect in terms of the works exerted by the boundary data when the inclusion is present or absent.

arXiv commentarXiv admin note: text overlap with arXiv:2209.08830

References in corpus (5)

• Nanomechanical Resonators and Their Applications in Biological/Chemical Detection: Nanomechanics Principles
• The stability for the Cauchy problem for elliptic equations
• The linear constraints in Poincaré and Korn type inequalities
• Size estimates for fat inclusions in an isotropic Reissner-Mindlin plate
• Doubling Inequality at the Boundary for the Kirchhoff -- Love Plate's Equation with Dirichlet Conditions