(High Frequency-) Uniqueness Criteria for \(p\)-Growth Functionals in in- and Compressible Elasticity

Abstract

In this work our main objective is to establish various (high frequency-) uniqueness criteria. Initially, we consider \(p\)-Dirichlet type functionals on a suitable class of measure preserving maps \(u: B\subset \mathbb{R}^{2} \to \mathbb{R}^{2}\), \(B\) being the unit disk, and subject to suitable boundary conditions. In the second part we focus on a very similar situations only exchanging the previous functionals by a suitable class of \(p\)-growing polyconvex functionals and allowing the maps to be arbitrary.

In both cases a particular emphasis is laid on high pressure situations, where only uniqueness for a subclass, containing solely of variations with high enough Fourier-modes, can be obtained.