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A theorem on geometric rigidity and the derivation of nonlinear plate theory from three‐dimensional elasticity

- G. Friesecke, R. James, S. Müller
- Mathematics
- 1 November 2002

The energy functional of nonlinear plate theory is a curvature functional for surfaces first proposed on physical grounds by G. Kirchhoff in 1850. We show that it arises as a Γ‐limit of… Expand

A Hierarchy of Plate Models Derived from Nonlinear Elasticity by Gamma-Convergence

- G. Friesecke, R. James, S. Müller
- Mathematics
- 2 January 2006

We derive a hierarchy of plate models from three-dimensional nonlinear elasticity by Γ-convergence. What distinguishes the different limit models is the scaling of the elastic energy per unit volume… Expand

Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit

- G. Friesecke, R. Pego
- Physics, Mathematics
- 1 November 1999

This paper is the first in a series to address questions of qualitative behaviour, stability and rigorous passage to a continuum limit for solitary waves in one-dimensional non-integrable lattices… Expand

Implicit time discretization and global existence for a quasi-linear evolution equation with nonconvex energy

- G. Friesecke, G. Dolzmann
- Mathematics
- 1 March 1997

We establish global existence of weak solutions for the viscoelastic system $u_{tt}=Div(\frac{\partial \Phi}{\partial F}(Du)+Du_t)$ with nonconvex stored-energy function $\Phi$. Unlike previous met...

Existence theorem for solitary waves on lattices

- G. Friesecke, J. Wattis
- Mathematics
- 1 March 1994

AbstractIn this article we give an existence theorem for localized travelling wave solutions on one-dimensional lattices with Hamiltonian
$$H = \sum\limits_{n \in \mathbb{Z}} {\left(… Expand

Validity and Failure of the Cauchy-Born Hypothesis in a Two-Dimensional Mass-Spring Lattice

- G. Friesecke, F. Theil
- MathematicsJ. Nonlinear Sci.
- 1 October 2002

TLDR

Density Functional Theory and Optimal Transportation with Coulomb Cost

- Codina Cotar, G. Friesecke, C. Klüppelberg
- Mathematics
- 4 April 2011

We present here novel insight into exchange‐correlation functionals in density functional theory, based on the viewpoint of optimal transport. We show that in the case of two electrons and in the… Expand

The Multiconfiguration Equations for Atoms and Molecules: Charge Quantization and Existence of Solutions

- G. Friesecke
- Mathematics
- 11 June 2003

We prove the existence of ground-state solutions for the multiconfiguration self-consistent field equations for atoms and molecules whenever the total nuclear charge Z exceeds N−1, where N is the… Expand

Dynamics as a mechanism preventing the formation of finer and finer microstructure

- G. Friesecke, J. McLeod
- Mathematics
- 1 September 1996

AbstractWe study the dynamics of pattern formation in the one-dimensional partial differential equation
$$u_u - (W'(u_x ))_x - u_{xxt} + u = 0{\text{ (}}u = u(x,t),{\text{ }}x \in (0,1),{\text{ }}t… Expand

A necessary and sufficient condition for nonattainment and formation of microstructure almost everywhere in scalar variational problems

- G. Friesecke
- MathematicsProceedings of the Royal Society of Edinburgh…
- 1994

For scalar variational problems subject to linear boundary values, we determine completely those integrands W: ℝn → ℝ for which the minimum is not attained, thereby completing previous efforts such… Expand

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