Flavia Giannetti

Estimates of Jacobians by subdeterminants

AbstractLet ƒ: Ω → ℝn be a mapping in the Sobolev space W1,n−1(Ω,ℝn), n ≥ 2. We assume that the determinant of the differential matrix Dƒ (x) is nonnegative, while the cofactor matrix D#ƒ satisfiesn

\infty

|D^sharp f|^{frac{n}{{n - 1}}} in L^P (Omega )

A remark on the L^1-lower semicontinuity for integral functionals in BV

n, where Lp(Ω) is an Orlicz space. We show that, under the natural Divergence Condition on P, see (1.10), the Jacobian lies in Lloc1 (Ω). Estimates above and below Lloc1 (Ω) are also studied. These results are stronger than the previously known estimates, having assumed integrability conditions on the differential matrix.

Isoperimetric type inequalities for differential forms on manifolds

Ihe central theme rnnning through our investigation la the on-Laplacian operator in the plane. Upon multiplication by a suitable funetion we express it in divergence form, this allows os to speak of weak no-harmonir funetion jo 4/1,2 lo every no-harmonir function u we associate its conjogate funetion e. We focus our attention to Ihe first order Beltrami type equation for h u + iv.