Some nonstandard-overdetermined boundary value problems for the biharmonic operator

Author

Teresa Jo Fouts

Date of Award

8-1994

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Phillip W. Schaefer

Committee Members

Don Hinton, Gary Simpson

Abstract

In the early seventies, Serrin considered an overdetermined boundary value problem and determined that if a solution exists, then the domain must be a ball. Many authors have then extended this result to other overdetermined problems. In this work, we first examine an overdetermined problem considered by Bennett and then consider three fourth order boundary value problems for the differential equation Δ₂u = f (r) in Ω. Two of the three auxiliary conditions are assumed to hold on the surface of a ball which is completely contained in Ω. Each auxiliary condition will be of a different type. We also show that Ω must be a ball. We then determine an integral representation of the solution for these problems.

Recommended Citation

Fouts, Teresa Jo, "Some nonstandard-overdetermined boundary value problems for the biharmonic operator. " Master's Thesis, University of Tennessee, 1994.
https://trace.tennessee.edu/utk_gradthes/11526