@article {2010, title = {Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity}, journal = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295}, number = {SISSA;12/2008/M}, year = {2010}, abstract = {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.}, doi = {10.2422/2036-2145.2010.2.02}, url = {http://hdl.handle.net/1963/2601}, author = {Marta Lewicka and Maria Giovanna Mora and Mohammad Reza Pakzad} } @article {2008, title = {A second order minimality condition for the Mumford-Shah functional}, journal = {Calc. Var. Partial Differential Equations 33 (2008) 37-74}, number = {SISSA;82/2006/M}, year = {2008}, abstract = {A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\\\\Gamma)$, $\\\\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\\\\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.}, doi = {10.1007/s00526-007-0152-3}, url = {http://hdl.handle.net/1963/1955}, author = {Filippo Cagnetti and Maria Giovanna Mora and Massimiliano Morini} }