A hunt for sharp Lp-Estimates and Rank-one Convex Variational Integrals

Kari Astala, Tadeusz Iwaniec, István Prause, Eero Saksman

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Learning how to figure out sharp Lp-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 martingale inequalities for stochastic integrals. Some of these topics have already been discussed by the present authors [5] and by Rodrigo Bãnuelos [10]. Nevertheless, there is always something new to add.

Original languageEnglish (US)
Pages (from-to)245-261
Number of pages17
JournalFilomat
Volume29
Issue number2
DOIs
StatePublished - 2015

Keywords

  • Critical Sobolev Exponents
  • Rank-one Convex and Quasiconvex Variational Integrals and Jacobian Inequalities

ASJC Scopus subject areas

  • Mathematics(all)

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