@article {2011,
	title = {The matching property of infinitesimal isometries on elliptic surfaces and elasticity on thin shells},
	journal = {Archive for Rational Mechanics and Analysis 200 (2011) 1023-1050},
	number = {SISSA;75/2008/M},
	year = {2011},
	publisher = {Springer},
	abstract = {Using the notion of Γ-convergence, we discuss the limiting behavior of the three-dimensional nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales like h β with 2 < β < 4. We establish that, for the given scaling regime, the limiting theory reduces to linear pure bending. Two major ingredients of the proofs are the density of smooth infinitesimal isometries in the space of W 2,2 first order infinitesimal isometries, and a result on matching smooth infinitesimal isometries with exact isometric immersions on smooth elliptic surfaces.},
	doi = {10.1007/s00205-010-0387-6},
	url = {http://hdl.handle.net/1963/3392},
	author = {Marta Lewicka and Maria Giovanna Mora and Mohammad Reza Pakzad}
}
@conference {10.1007/978-1-4419-9554-4_10,
	title = {The Monge Problem in Geodesic Spaces},
	booktitle = {Nonlinear Conservation Laws and Applications},
	year = {2011},
	pages = {217{\textendash}233},
	publisher = {Springer US},
	organization = {Springer US},
	address = {Boston, MA},
	abstract = {<p>We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish non branching geodesic space. We show that we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce an assumption on the transport problem π which implies that the conditional probabilities of the first marginal on each geodesic are continuous. It is known that this regularity is sufficient for the construction of an optimal transport map.</p>},
	isbn = {978-1-4419-9554-4},
	author = {Stefano Bianchini and Fabio Cavalletti},
	editor = {Alberto Bressan and Chen, Gui-Qiang G. and Marta Lewicka and Wang, Dehua}
}
