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Annalisa Baldi

Associate Professor

Department of Mathematics

Academic discipline: MAT/05 Mathematical Analysis


Keywords: Compensated compactness Carnot groups Differential forms Poincaré Inequalities Homogenization

Intrinsic currents and differential intrinsic forms in Carnot groups. Subelliptic partial differential equations. Homogenization for differential operators in Carnot groups. Maxwell Equations in Carnot groups. Uniform rectifiability in Heisenberg group.

i)Differential forms in Carnot groups and differential operators on forms: in collaboration
with B. Franchi and M.C. Tesi we plan to develop a L^p theory of intrinsic differential
forms in Carnot groups and to study Maxwell system in groups. Moreover,  in collaboration with B.
Franchi, N. Tchou and M.C. Tesi we plan to carry on the study of the homogenization of
differential operators in Carnot groups via compensated compactness methods.
ii)Integral inequalities in Carnot groups: I plan to extend to intrinsic differential forms
in Carnot groups a chain of Poincaré-type inequalities proved recently by Lanzani & Stein
for De Rham differential forms. iii) A Rademacher-type theorem for intrinsic Lischitz graphs is carried out by Franchi, Serapioni and Serra Cassano. In collaboration with N. Arcozzi, we try to extend to the Heisenberg group a notion of uniform rectifiability.

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