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Full-Text Articles in Physical Sciences and Mathematics
An Introduction To Obstacle Problems, Calvin Reedy
An Introduction To Obstacle Problems, Calvin Reedy
Honors Theses
The obstacle problem can be used to predict the shape of an elastic membrane lying over an obstacle in a domain Ω. In this paper we introduce and motivate a mathematical formulation for this problem, and give an example to demonstrate the need to search for solutions in non-classical settings. We then introduce Sobolev spaces as the proper setting for solutions, and prove that unique solutions exist in W1,2(Ω).
Banach Spaces Of Analytic Functions, Michael T. Nimchek
Banach Spaces Of Analytic Functions, Michael T. Nimchek
Honors Theses
In this paper, we explore certain Banach spaces of analytic functions. In particular, we study the space A-1, demonstrating some of its basic properties including non-separability. We ask the question: given a class C of analytic functions on the unit disk D and a sequence [Zn] = 0 for all n? Finally, we explore Mz invariant subspaces of A-1, demonstrating that they may possess the codimension-2 property.