{"paper":{"title":"Burkholder integrals, Morrey's problem and quasiconformal mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Eero Saksman, Istv\\'an Prause, Kari Astala, Tadeusz Iwaniec","submitted_at":"2010-12-02T17:13:12Z","abstract_excerpt":"Inspired by Morrey's Problem (on rank-one convex functionals) and the Burkholder integrals (of his martingale theory) we find that the Burkholder functionals $B_p$, $p \\ge 2$, are quasiconcave, when tested on deformations of identity $f\\in Id + C^\\infty_0(\\Omega)$ with $B_p(Df(x)) \\ge 0$ pointwise, or equivalently, deformations such that $|Df|^2 \\leq \\frac{p}{p-2} J_f$. In particular, this holds in explicit neighbourhoods of the identity map. Among the many immediate consequences, this gives the strongest possible $L^p$- estimates for the gradient of a principal solution to the Beltrami equati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0504","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}