In his pioneering work, Jacobi discovered two remarkable identities related to the Jacobian.
The first one asserts that the Jacobian has a divergence structure. The second one, that …

Minimal lifting measures of vector-valued functions of bounded variation were introduced by
Jerrard–Jung. They satisfy strong continuity properties with respect to the strict convergence …

For surfaces without boundary, nonlocal notions of directional and mean curvatures have
been recently given. Here, we develop alternative notions, special cases of which apply to …

H. Brezis and L. Nirenberg proved that if (gk)⊂ C⁰ (𝕊 N, 𝕊 N) and g∈ C⁰ (𝕊 N, 𝕊 N)(N≥ 1)
are such that gk→ g in BMO (𝕊 N), then deg gk→ deg g. On the other hand, if g∈ C¹ (𝕊 N, 𝕊 …

In the literature various notions of nonlocal curvature can be found. Here we propose a
notion of nonlocal curvature tensor. This we do by generalizing an appropriate …

Sobolev spaces W^{s, p}(Ω; N) of maps to compact Riemannian manifolds N do not enjoy
the standard properties of scalar Sobolev spaces; for example, approximability with smooth …

This thesis concerns the mathematical analysis of some hydrodynamic models describing
quantum fluids, namely fluids whose macroscopic behavior still exhibits quantum effects …

Calculus of Variations — A notion of nonlocal Gaussian curvature, by Paolo Podio-Guidugli,
communicated on 13 November 2015. D Page 1 Rend. Lincei Mat. Appl. 27 (2016), 181–193 …

We deal with integral currents in Cartesian products of Euclidean spaces that satisfy a
“verticality” assumption. The main example is the boundary of the graph of some classes …

Prescribed singularities with weights Page 1 Adv. Nonlinear Anal. 1 (2012), 355 – 381 DOI
10.1515/anona-2012-0015 © de Gruyter 2012 Prescribed singularities with weights Ioana A …