A hunt for sharp $L ^p$-estimates and rank-one convex variational integrals
Complex Variables
2015-08-24 v1
Abstract
Learning how to figure out sharp -estimates of nonlinear differential expressions, to prove and use them, is a fundamental part of the development of PDEs and Geometric Function Theory (GFT). Our survey presents, among what is known to date, some notable recent efforts and novelties made in this direction. We focus attention here on the historic Morrey's Conjecture and Burkholder's martingale inequalities for stochastic integrals. Some of these topics have already been discussed by the present authors [5] and by Rodrigo Ba\~{n}uelos [10]. Nevertheless, there is always something new to add.
Cite
@article{arxiv.1403.1095,
title = {A hunt for sharp $L ^p$-estimates and rank-one convex variational integrals},
author = {Kari Astala and Tadeusz Iwaniec and István Prause and Eero Saksman},
journal= {arXiv preprint arXiv:1403.1095},
year = {2015}
}
Comments
24 pages