Date of Award
Bachelor of Science
Dr. Jeremy LeCrone
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).
Reedy, Calvin, "An Introduction to Obstacle Problems" (2021). Honors Theses. 1553.