Date of Award
5-10-2026
Date Published
June 2026
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
Advisor(s)
Jani Onninen
Keywords
Energy;Global invertibility;Sobolev
Subject Categories
Mathematics | Physical Sciences and Mathematics
Abstract
We prove two main results at the intersection of Geometric Function Theory and Nonlinear Elasticity. The first is a Sobolev variant of the Inverse Function Theorem, which generalizes a famous result of John Ball. It uses Classical Sobolev Theory as well as the Degree Function, which was initially a topological tool. The second result is the existence and uniqueness (up to rotation) of a radially-symmetric minimizer for Sobolev mappings with prescribed Jacobian. This result generalizes recent work of André Guerra, Lukas Koch, and Sauli Lindberg.
Access
Open Access
Recommended Citation
Traver, Sabrina, "Global Invertibility of Sobolev Mappings and Energy Minimizers with Prescribed Jacobian" (2026). Dissertations - ALL. 2289.
https://surface.syr.edu/etd/2289
