TY - THES
T1 - Dimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms
Y1 - 2011
A1 - Sara Daneri
AB - This thesis is devoted to the study of two different problems: the properties of the disintegration of the Lebesgue measure on the faces of a convex function and the existence of smooth approximations of bi-Lipschitz orientation-preserving homeomorphisms in the plane.
PB - SISSA
UR - http://hdl.handle.net/1963/5348
U1 - 5178
U2 - Mathematics
U3 - Functional Analysis and Applications
U4 - -1
ER -
TY - JOUR
T1 - The disintegration of the Lebesgue measure on the faces of a convex function
JF - J. Funct. Anal. 258 (2010) 3604-3661
Y1 - 2010
A1 - Laura Caravenna
A1 - Sara Daneri
AB - We consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets.

UR - http://hdl.handle.net/1963/3622
U1 - 682
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -