A Class of Functions That Are Quasiconvex But Not Polyconvex

Author

Catherine S. Remus, University of Tennessee - Knoxville

Date of Award

12-2003

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Henry C. Simpson

Committee Members

Charles Collins, G. Samuel Jordan

Abstract

In 1991 V. Sverak [11] gave an example of a function that was invariant and quasiconvex but not polyconvex. We have generalized this example to a wide class of functions that meet certain ellipticity and growth conditions. Quasiconvexity is one necessary and sufficient condition for the existence of solutions to the minimization problem in elliptic P.D.E. theory. Invariance is frequently a requirement of the stored energy function in Calculus of Variation approaches to elasticity problems.

Recommended Citation

Remus, Catherine S., "A Class of Functions That Are Quasiconvex But Not Polyconvex. " Master's Thesis, University of Tennessee, 2003.
https://trace.tennessee.edu/utk_gradthes/2219