A strictly convex Sobolev function with null Hessian minors
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10335022" target="_blank" >RIV/00216208:11320/16:10335022 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00526-016-0994-7" target="_blank" >http://dx.doi.org/10.1007/s00526-016-0994-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00526-016-0994-7" target="_blank" >10.1007/s00526-016-0994-7</a>
Alternative languages
Result language
angličtina
Original language name
A strictly convex Sobolev function with null Hessian minors
Original language description
Given 1 LESS-THAN OR EQUAL TO p < k LESS-THAN OR EQUAL TO n, we construct a strictly convex function f ELEMENT OF W^{2,p}((0,1)^n) with α-Hölder continuous derivative for any 0 < α < 1 such that rank NABLA^2 f < k almost everywhere in (0, 1)^n. In particular, the mapping F = NABLA f is an example of a W^{1,p} homeomorphism whose differential has rank strictly less than k almost everywhere in the unit cube. This Sobolev regularity is sharp in the sense that if g ELEMENT OF W^{2,p}, p GREATER-THAN OR EQUAL TO k, and rank NABLA^2 g < k a.e., then g cannot be strictly convex on any open portion of the domain.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Calculus of Variations and Partial Differential Equations
ISSN
0944-2669
e-ISSN
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Volume of the periodical
55
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
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UT code for WoS article
000377830200015
EID of the result in the Scopus database
2-s2.0-84971324334