Monotone Hopf-Harmonics
Publiceringsår
2020
Upphovspersoner
Iwaniec, Tadeusz; Onninen, Jani
Abstrakt
We introduce the concept of monotone Hopf-harmonics in 2D as an alternative to harmonic homeomorphisms. Much of the foregoing is motivated by the principle of non-interpenetration of matter in the mathematical theory of Nonlinear Elasticity (NE). The question we are concerned with is whether or not a Dirichlet energy-minimal mapping between Jordan domains with a prescribed boundary homeomorphism remains injective in the domain. The classical theorem of Radó–Kneser–Choquet asserts that this is the case when the target domain is convex. An alternative way to deal with arbitrary target domains is to minimize the Dirichlet energy subject to only homeomorphisms and their limits. This leads to the so called Hopf–Laplace equation. Among its solutions (some rather surreal) are continuous monotone mappings of Sobolev class W1,2 loc , called monotone Hopf-harmonics. It is at the heart of the present paper to show that such solutions are correct generalizations of harmonic homeomorphisms and, in particular, are legitimate deformations of hyperelastic materials in the modern theory of NE. We make this clear by means of several examples.
Visa merOrganisationer och upphovspersoner
Jyväskylä universitet
Onninen Jani
Publikationstyp
Publikationsform
Artikel
Moderpublikationens typ
Tidning
Artikelstyp
En originalartikel
Målgrupp
VetenskapligKollegialt utvärderad
Kollegialt utvärderadUKM:s publikationstyp
A1 Originalartikel i en vetenskaplig tidskriftPublikationskanalens uppgifter
Förläggare
Volym
237
Nummer
2
Sidor
743-777
ISSN
Publikationsforum
Publikationsforumsnivå
3
Öppen tillgång
Öppen tillgänglighet i förläggarens tjänst
Nej
Parallellsparad
Nej
Övriga uppgifter
Vetenskapsområden
Matematik
Nyckelord
[object Object],[object Object],[object Object]
Publiceringsland
Tyskland
Förlagets internationalitet
Internationell
Språk
engelska
Internationell sampublikation
Ja
Sampublikation med ett företag
Nej
DOI
10.1007/s00205-020-01518-2
Publikationen ingår i undervisnings- och kulturministeriets datainsamling
Ja