DeepAI

# The Elasticity Complex

We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For the involved tensor fields and operators we show closed ranges, Friedrichs/Poincare type estimates, Helmholtz type decompositions, regular decompositions, regular potentials, finite cohomology groups, and, most importantly, new compact embedding results. Our results hold for general bounded strong Lipschitz domains of arbitrary topology and rely on a general functional analysis framework (FA-ToolBox).

• 3 publications
• 4 publications
03/22/2020

### Symmetric Tensor Decompositions On Varieties

This paper discusses the problem of symmetric tensor decomposition on a ...
06/29/2022

### Generalized Pseudoskeleton Decompositions

We characterize some variations of pseudoskeleton (also called CUR) deco...
06/29/2021

### Interaction of Multiple Tensor Product Operators of the Same Type: an Introduction

Tensor product operators on finite dimensional Hilbert spaces are studie...
12/17/2019

### Tensor Rank bounds for Point Singularities in R^3

We analyze rates of approximation by quantized, tensor-structured repres...
06/24/2021

### The condition number of many tensor decompositions is invariant under Tucker compression

We characterise the sensitivity of several additive tensor decomposition...
05/25/2020

### Complexes from complexes

This paper is concerned with the derivation and properties of differenti...
06/06/2021

### Singular Dynamic Mode Decompositions

This manuscript is aimed at addressing several long standing limitations...