L1

In this talk we will discuss a theory of divergence-measure fields and related

geometric measures, developed recently, and its applications to some fundamental

issues in mathematical continuum physics and nonlinear conservation laws whose

solutions have very weak regularity, including hyperbolic conservation laws,

degenerate parabolic equations, degenerate elliptic equations, among others.

Let M be an ordered vector space over an ordered division ring, and G a definably compact, definably connected group definable in M. We show that G is definably isomorphic to a definable quotient U/L, where U is a convex subgroup of M^n and L is a Z-lattice of rank n. This is a joint work with Panelis Eleftheriou.

/notices/events/abstracts/applied-analysis/tt05/Heywood.pdf

We derive a two-dimensional compressible elasticity model for thin elastic sheets as a Gamma-limit of a fully three-dimensional incompressible theory. The energy density of the reduced problem is obtained in two

steps: first one optimizes locally over out-of-plane deformations, then one passes to the quasiconvex envelope of the resulting energy density. This work extends the results by LeDret and Raoult on smooth and finite-valued energies to the case incompressible materials. The main difficulty in this extension is the construction of a recovery sequence which satisfies the nonlinear constraint of incompressibility pointwise everywhere.

This is joint work with Sergio Conti.