51 citations · 416 across the 43 of their papers we have counts for
6 papers · 1 filter
Integration of nonsmooth -forms: from Young to Itô and Stratonovich
Giovanni Alberti, Eugene Stepanov, Dario Trevisan
We show that geometric integrals of the type can be defined over a two-dimensional domain when the functions , , $g^2\colon \mathbb{R}^…
On the geometric structure of currents tangent to smooth distributions
Giovanni Alberti, Annalisa Massaccesi, Eugene Stepanov
It is well known that a k-dimensional smooth surface in a Euclidean space cannot be tangent to a non-involutive distribution of k-dimensional planes. In this paper we discuss the e…
Infinite-dimensional inverse problems with finite measurements
Giovanni S. Alberti, Matteo Santacesaria
We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measu…
Optimal reinforcing networks for elastic membranes
Giovanni Alberti, Giuseppe Buttazzo, Serena Guarino Lo Bianco +1
In this paper we study the optimal reinforcement of an elastic membrane, fixed at its boundary, by means of a network (connected onedimensional structure), that has to be found in…
Combining the Runge approximation and the Whitney embedding theorem in hybrid imaging
Giovanni S. Alberti, Yves Capdeboscq
This paper addresses enforcing non-vanishing constraints for solutions to a second order elliptic partial differential equation by appropriate choices of boundary conditions. We sh…
On the randomised stability constant for inverse problems
Giovanni S. Alberti, Yves Capdeboscq, Yannick Privat
In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the c…