Giuseppe Di Fazio

Poisson Equations and Morrey Spaces

< i. < n. (For the precise statement see Section 1). The solution we consider is a very weak one introduced in [LSW] because in general the Dirichlet problem for Eq. (*) does not have a weak (variational) solution under our assumption onf. The purpose of our work is to study the regularity properties of the solu- tion as the parameter A increases from 0 to n. In fact we prove

A Fefferman-Poincaré type inequality for Carnot-Carathéodory vector fields

In this note we prove a Fefferman-Poincare type inequality in spaces with metric induced by Carnot-Caratheodory vector fields.

Sum Operators and Fefferman–Phong Inequalities

We define Stummel-Kato type classes in a quasimetric homogeneous setting using sum operators introduced in (J. Fourier Anal. Appl. 9(5), 511–540, 2003) by Franchi, Perez and Wheeden. Then we prove an embedding inequality of Fefferman–Phong type. As an application we give a unique continuation result for non negative solutions of some subelliptic equations.

Stable determination of a Lamé coefficient by one internal measurement of displacement

Abstract In this paper we show that the shear modulus μ of an isotropic elastic body can be stably recovered by the knowledge of one single displacement field whose boundary data can be assigned independently on the unknown elasticity tensor.