Title page for ETD etd-052409-201502

Document Type thesis

Author Name Owens, Will

URN etd-052409-201502

Title Finite Energy Functional Spaces on Unbounded Domains with a Cut

Degree MS

Department Mathematical Sciences

Advisors
Darko Volkov, Advisor
Bogdan M. Vernescu, Department Head

Keywords
finite energy functional spaces
unbounded domains with a cut

Date of Presentation/Defense 2009-05-24

Availability unrestricted

Abstract
Abstract We study in this thesis functional spaces involved in crack problems in unbounded domains. These spaces are defined by closing spaces of Sobolev H¹ regularity functions (or vector fields) of bounded support, by the L² norm of the gradient. In the case of linear elasticity, the closure is done under the L² norm of the symmetric gradient. Our main result states that smooth functions are in this closure if and only if their gradient, (respectively symmetric gradient for the elasticity case), is in L². We provide examples of functions in these newly defined spaces that are not in L². We show however that some limited growth in dimension 2, or some decay in dimension 3 must hold for functions in those spaces: this is due to Hardy's inequalities.

Files
wowens.pdf

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Document Type	thesis
Author Name	Owens, Will
URN	etd-052409-201502
Title	Finite Energy Functional Spaces on Unbounded Domains with a Cut
Degree	MS
Department	Mathematical Sciences
Advisors	Darko Volkov, Advisor Bogdan M. Vernescu, Department Head
Keywords	finite energy functional spaces unbounded domains with a cut
Date of Presentation/Defense	2009-05-24
Availability	unrestricted
Abstract Abstract We study in this thesis functional spaces involved in crack problems in unbounded domains. These spaces are defined by closing spaces of Sobolev H¹ regularity functions (or vector fields) of bounded support, by the L² norm of the gradient. In the case of linear elasticity, the closure is done under the L² norm of the symmetric gradient. Our main result states that smooth functions are in this closure if and only if their gradient, (respectively symmetric gradient for the elasticity case), is in L². We provide examples of functions in these newly defined spaces that are not in L². We show however that some limited growth in dimension 2, or some decay in dimension 3 must hold for functions in those spaces: this is due to Hardy's inequalities.
Files	wowens.pdf