Title
Mappings of finite distortion and values of finite distortions
Abstract
In this talk, we are concerned with mappings of finite distortion and values of finite distortion, with emphasis on questions arising in geometric function theory and nonlinear elasticity.
First, we present a uniqueness result for minimizers of the planar Lp-mean distortion among diffeomorphisms with prescribed boundary values. Next, we describe a global logarithmic integrability estimate for the reciprocal Jacobian of homeomorphisms of finite distortion between suitable higher-dimensional domains. As an application, we show that weak limits of homeomorphisms between Lipschitz domains with uniformly bounded L1/(n-1)-mean distortion satisfy the Sobolev (INV) condition. Finally, we consider mappings with a value of finite distortion at a point y0 with data (K,Σ), as well as mappings satisfying the (K,Σ)-distortion inequality with defect, proving the Lusin (N)-property for both classes and a single-value version of Reshetnyak's theorem for the former.
