0000000000347073

AUTHOR

Carlo Sbordone

MAPPINGS OF FINITE DISTORTION: $L^n \log^{\alpha} L$ -INTEGRABILITY

Recently, systematic studies of mappings of finite distortion have emerged as a key area in geometric function theory. The connection with deformations of elastic bodies and regularity of energy minimizers in the theory of nonlinear elasticity is perhaps a primary motivation for such studies, but there are many other applications as well, particularly in holomorphic dynamics and also in the study of first order degenerate elliptic systems, for instance the Beltrami systems we consider here.

research product

Anisotropic Sobolev homeomorphisms

Let › ‰ R 2 be a domain. Suppose that f 2 W 1;1 loc (›;R 2 ) is a homeomorphism. Then the components x(w), y(w) of the inverse f i1 = (x;y): › 0 ! › have total variations given by jryj(› 0 ) = › fl fl @f fl fl dz; jrxj(› 0 ) = › fl fl @f @y fl fl dz:

research product