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 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.
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