C2-Regularity for Partially Free Minimal Surfaces.
Caccioppoli sets
The story of the theory of Caccioppoli sets is presented, together with some information about Renato Caccioppoli’s life. The fundamental contributions of Ennio De Giorgi to the theory of Caccioppoli sets are sketched. A list of applications of Cacciopoli sets to the calculus of variations is finally included.
Calibrations and the size of Grassmann faces.
Capillary Surfaces in Negative Gravitational Fields.
Capillary surfaces in non-cylindrical domains.
Cartesian currents and variational problems for mappings into spheres
Cartesian currents in the calculus of variations
Chaînes holomorphes de bord donné dans
Characterization and representation of the lower semicontinuous envelope of the elastica functional
Characterization of homogeneous gradient young measures in case of arbitrary integrands
Characterization of optimal shapes and masses through Monge-Kantorovich equation
We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both cases some examples are presented.
Checkerboards, Lipschitz functions and uniform rectifiability.
In his recent lecture at the International Congress [S], Stephen Semmes stated the following conjecture for which we provide a proof.Theorem. Suppose Ω is a bounded open set in Rn with n > 2, and suppose that B(0,1) ⊂ Ω, Hn-1(∂Ω) = M < ∞ (depending on n and M) and a Lipschitz graph Γ (with constant L) such that Hn-1(Γ ∩ ∂Ω) ≥ ε.Here Hk denotes k-dimensional Hausdorff measure and B(0,1) the unit ball in Rn. By iterating our proof we obtain a slightly stronger result which allows us...
Clusters minimizing area plus length of singular curves.
Coalescence of measures and f-rearrangements of a function.
Coincidence set of minimal surfaces for the thin obstacle.
Commutative neutrix convolution products of functions
The commutative neutrix convolution product of the functions and is evaluated for and all . Further commutative neutrix convolution products are then deduced.
Compactness of Special Functions of Bounded Higher Variation
Given an open set Ω ⊂ Rm and n > 1, we introduce the new spaces GBnV(Ω) of Generalized functions of bounded higher variation and GSBnV(Ω) of Generalized special functions of bounded higher variation that generalize, respectively, the space BnV introduced by Jerrard and Soner in [43] and the corresponding SBnV space studied by De Lellis in [24]. In this class of spaces, which allow as in [43] the description of singularities of codimension n, the distributional jacobian Ju need not have finite...
Comparing homologies: Cech's theory, singular chains, integral flat chains and integral currents.
Comparison of Hausdorff measures with respect to the Euclidean and the Heisenberg metric.
We compare the Hausdorff measures and dimensions with respect to the Euclidean and Heisenberg metrics on the first Heisenberg group. The result is a dimension jump described by two inequalities. The sharpness of our estimates is shown by examples. Moreover a comparison between Euclidean and H-rectifiability is given.
Comparison principles and Liouville theorems for prescribed mean curvature equations in unbounded domains