TY - RPRT T1 - Dimension reduction for thin films with transversally varying prestrain: the oscillatory and the non-oscillatory case Y1 - 2018 A1 - Marta Lewicka A1 - Danka Lučić ER - TY - JOUR T1 - The matching property of infinitesimal isometries on elliptic surfaces and elasticity on thin shells JF - Archive for Rational Mechanics and Analysis 200 (2011) 1023-1050 Y1 - 2011 A1 - Marta Lewicka A1 - Maria Giovanna Mora A1 - Mohammad Reza Pakzad AB - 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. PB - Springer UR - http://hdl.handle.net/1963/3392 U1 - 940 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CONF T1 - The Monge Problem in Geodesic Spaces T2 - Nonlinear Conservation Laws and Applications Y1 - 2011 A1 - Stefano Bianchini A1 - Fabio Cavalletti ED - Alberto Bressan ED - Chen, Gui-Qiang G. ED - Marta Lewicka ED - Wang, Dehua AB -

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.

JF - Nonlinear Conservation Laws and Applications PB - Springer US CY - Boston, MA SN - 978-1-4419-9554-4 ER - TY - JOUR T1 - Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity JF - Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295 Y1 - 2010 A1 - Marta Lewicka A1 - Maria Giovanna Mora A1 - Mohammad Reza Pakzad AB - We discuss the limiting behavior (using the notion of gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h4, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Karman theory for plates. UR - http://hdl.handle.net/1963/2601 U1 - 1521 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A nonlinear theory for shells with slowly varying thickness JF - C. R. Math. 347 (2009) 211-216 Y1 - 2009 A1 - Marta Lewicka A1 - Maria Giovanna Mora A1 - Mohammad Reza Pakzad AB - We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface. UR - http://hdl.handle.net/1963/2632 U1 - 1491 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Uniqueness Condition for Hyperbolic Systems of Conservation Laws JF - Discrete Contin. Dynam. Systems 6 (2000) 673-682 Y1 - 2000 A1 - Alberto Bressan A1 - Marta Lewicka AB - Consider the Cauchy problem for a hyperbolic $n\\\\times n$ system of conservation laws in one space dimension: $$u_t+f(u)_x=0, u(0,x)=\\\\bar u(x).\\\\eqno(CP)$$ Relying on the existence of a continuous semigroup of solutions, we prove that the entropy admissible solution of (CP) is unique within the class of functions $u=u(t,x)$ which have bounded variation along a suitable family of space-like curves. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3195 U1 - 1106 U2 - Mathematics U3 - Functional Analysis and Applications ER -