Antonino Morassi

We establish boundedness of solutions to a class of two-weight degenerate elliptic equations, which is motivated by the mechanical model of a spider orb web introduced in Morassi, Soler, and Zaera [ Mech. Syst. Signal Process., 93 (2017), pp. 610–633]. Our results extends the classical boundedness framework to nonuniformly elliptic equations with two weights and covers, in particular, the equation governing the static equilibrium of the spider orb web membrane model.

We study the inverse problem of determining the Winkler coefficient in a nanoplate resting on an elastic foundation and clamped at the boundary. The nanoplate is described within a simplified strain gradient elasticity theory for isotropic materials, under the Kirchhoff–Love kinematic assumptions in infinitesimal deformation. We prove a global Hölder stability estimate of the subgrade coefficient by performing a single interior measurement of the transverse deflection of the nanoplate induced by a load concentrated at one point.

We study the inverse problem of determining the Winkler coefficient in a nanoplate resting on an elastic foundation and clamped at the boundary. The nanoplate is described within a simplified strain gradient elasticity theory for isotropic materials, under the Kirchhoff-Love kinematic assumptions in infinitesimal deformation. We prove a global Hölder stability estimate of the subgrade coefficient by performing a single interior measurement of the transverse deflection of the nanoplate induced by a load concentrated at one point.