• Corpus ID: 233714793

# Extremal mappings of finite distortion and the Radon-Riesz property

@inproceedings{Martin2021ExtremalMO,
title={Extremal mappings of finite distortion and the Radon-Riesz property},
author={Gaven J. Martin and Cong Yao},
year={2021}
}
• Published 3 May 2021
• Mathematics
We consider Sobolev mappings f ∈ W (Ω,C), 1 < q < ∞, between planar domains Ω ⊂ C. We analyse the Radon-Riesz property for convex functionals of the form f 7→ ∫ Ω Φ(|Df(z)|, J(z, f)) dz and show that under certain criteria, which hold in important cases, weak convergence in W 1,q loc (Ω) of (for instance) a minimising sequence can be improved to strong convergence. This finds important applications in the minimisation problems for mappings of finite distortion and the L and Exp -Teichmüller…
1 Citations
The Teichm\"uller problem for $L^p$-means of distortion
• Mathematics
• 2021
Teichmüller’s problem from 1944 is this: Given x ∈ [0, 1) find and describe the extremal quasiconformal map f : D → D, f |∂D = identity and f(0) = −x ≤ 0. We consider this problem in the setting of

## References

SHOWING 1-10 OF 18 REFERENCES
Extremal mappings of finite distortion
• Mathematics
• 2005
The theory of mappings of finite distortion has arisen out of a need to extend the ideas and applications of the classical theory of quasiconformal mappings to the degenerate elliptic setting where
Deformations of Annuli with Smallest Mean Distortion
• Mathematics
• 2010
We determine the extremal mappings with smallest mean distortion for mappings of annuli. As a corollary, we find that the Nitsche harmonic maps are Dirichlet energy minimizers among all
Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Pms-48)
• Mathematics
• 2009
This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis.
Non-variational extrema of exponential Teichmüller spaces
• Mathematics
Complex Analysis and its Synergies
• 2021
The exponential Teichmuller spaces $E_p$, $0\leq p \leq \infty$, interpolate between the classical Teichmuller space ($p=\infty$) and the space of harmonic diffeomorphisms $(p=0)$. In this article we
Optimal regularity for planar mappings of finite distortion
• Mathematics
• 2008
Let $f:\Omega\to\IR^2$ be a mapping of finite distortion, where $\Omega\subset\IR^2 .$ Assume that the distortion function $K(x,f)$ satisfies $e^{K(\cdot, f)}\in L^p_{loc}(\Omega)$ for some $p>0.$ We
The Nitsche conjecture
• Mathematics
• 2009
The Nitsche conjecture is deeply rooted in the theory of doubly connected minimal surfaces. However, it is commonly formulated in slightly greater generality as a question of existence of a harmonic
Smoothing Defected Welds and Hairline Cracks
• Mathematics, Computer Science
SIAM J. Math. Anal.
• 2016
Let a smooth curve (hairline crack) split a planar domain into two pieces. We consider a homeomorphism of the domain (hyperelastic deformation), which is a diffeomorphism on each side of the curve.
The $L^p$ Teichm\"uller theory: Existence and regularity of critical points
• Mathematics
• 2020
We study minimisers of the $p$-conformal energy functionals, $\mathsf{E}_p(f):=\int_\ID \IK^p(z,f)\,dz,\quad f|_\IS=f_0|_\IS,$ defined for self mappings $f:\ID\to\ID$ with finite distortion and
An Introduction to Banach Space Theory
1 Basic Concepts.- 1.1 Preliminaries.- 1.2 Norms.- 1.3 First Properties of Normed Spaces.- 1.4 Linear Operators Between Normed Spaces.- 1.5 Baire Category.- 1.6 Three Fundamental Theorems.- 1.7
An Introduction to Partial Differential Equations
The field of partial differential equations (PDEs) is vast in size and diversity. The basic reason for this is that essentially all fundamental laws of physics are formulated in terms of PDEs. In