Název: Vlastnosti zobrazení s konečnou distorzí
Překlad názvu: Properties of mappings of finite distortion
Autoři: Campbell, Daniel ; Hencl, Stanislav (vedoucí práce)
Typ dokumentu: Rigorózní práce
Rok: 2018
Jazyk: eng
Abstrakt: In the following thesis we will be mostly concerned with questions related to the regularity of solutions to non-linear elasticity models in the calculus of variations. An important step in this is question is the approximation of Sobolev homeomorphisms by diffeomorphisms. We refine an approximation result of Hencl and Pratelli's which, for a given planar Sobolev (or Sobolev-Orlicz) homeomorphism, constructs a diffeomorphism arbitrarily close to the original map in uniform convergence and in terms of the Sobolev-Orlicz norm. Further we show, in dimension 4 or higher, that such an approximation result cannot hold in Sobolev spaces W1,p where p is too small by constructing a sense-preserving homeomorphism with Jacobian negative on a set of positive measure. The class of mappings referred to as mappings of finite distortion have been proposed as possible models for deformations of bodies in non-linear elasticity. In this context a key property is their continuity. We show, by counter-example, the surprising sharpness of the modulus of continuity with respect to the integrability of the distortion function. Also we prove an optimal regularity result for the inverse of a bi-Lipschitz Sobolev map in Wk,p and composition of Lipschitz maps in Wk,p comparable with the classical inverse mapping theorem. As a...
Klíčová slova: otevřenost a diskrétnost; Zobrazení s konečnou distorzí; Mapping of finite distortion; openess and disreteness

Instituce: Fakulty UK (VŠKP) (web)
Informace o dostupnosti dokumentu: Dostupné v digitálním repozitáři UK.
Původní záznam: http://hdl.handle.net/20.500.11956/104294

Trvalý odkaz NUŠL: http://www.nusl.cz/ntk/nusl-391338


Záznam je zařazen do těchto sbírek:
Školství > Veřejné vysoké školy > Univerzita Karlova > Fakulty UK (VŠKP)
Vysokoškolské kvalifikační práce > Rigorózní práce
 Záznam vytvořen dne 2019-01-07, naposledy upraven 2019-01-07.


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