Faculty Advisor or Committee Member

Darko Volkov, Advisor

Faculty Advisor or Committee Member

Bogdan M. Vernescu

Identifier

etd-052409-201502

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.

Publisher

Worcester Polytechnic Institute

Degree Name

MS

Department

Mathematical Sciences

Project Type

Thesis

Date Accepted

2009-05-24

Accessibility

Unrestricted

Subjects

finite energy functional spaces, unbounded domains with a cut, Function spaces

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