Currently displaying 1 – 18 of 18

Showing per page

Order by Relevance | Title | Year of publication

Convex integration with constraints and applications to phase transitions and partial differential equations

Stefan MüllerVladimír Šverák — 1999

Journal of the European Mathematical Society

We study solutions of first order partial differential relations D u K , where u : Ω n m is a Lipschitz map and K is a bounded set in m × n matrices, and extend Gromov’s theory of convex integration in two ways. First, we allow for additional constraints on the minors of D u and second we replace Gromov’s P −convex hull by the (functional) rank-one convex hull. The latter can be much larger than the former and this has important consequences for the existence of ‘wild’ solutions to elliptic systems. Our work was originally...

Sufficient conditions for the validity of the Cauchy-Born rule close to SO ( n )

Sergio ContiGeorg DolzmannBernd KirchheimStefan Müller — 2006

Journal of the European Mathematical Society

The Cauchy–Born rule provides a crucial link between continuum theories of elasticity and the atomistic nature of matter. In its strongest form it says that application of affine displacement boundary conditions to a monatomic crystal will lead to an affine deformation of the whole crystal lattice. We give a general condition in arbitrary dimensions which ensures the validity of the Cauchy–Born rule for boundary deformations which are close to rigid motions. This generalizes results of Friesecke...

Page 1

Download Results (CSV)