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.
