Mappings Between Annuli of Smallest p-Harmonic Energy

<p>An important topic in the calculus of variations is the study of traction-free problems, in which deformations between given domains in \mathbb{R}ⁿ are allowed to slip on the boundary, without prescribing boundary values. For annuli $\A = \A(r, R)$ and \A^* = \A(r_*, R_*), we seek the traction-free minimizer of the $p$-harmonic energy among homeomorphisms in Sobolev class W^{1, p}(\A, \A^*). For such a mapping, the $p$-harmonic energy is defined by \begin{equation*}</p> <p>\mathcal{E}_p[h] = \int\limits_{\A} |Dh(x)|^p dx</p> <p>\end{equation*} </p> <p>Classical methods fail for traction-free problems. We will use a novel approach based on the concept of free Lagrangians, described as differential forms $L(x, h(x), Dh(x))dx$ whose integral depends only on the homotopy class of $h$. We find that the solution to the $p$-harmonic variational problem depends on the relative thickness of $\A$ and \A^*.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year

2017

Author dc:creator

• Cuneo, Daniel

Contributors dc:contributor

• Tadeusz Iwaniec

• calculus of variations
• free Lagrangian
• p-harmonic energy
• Physical Sciences and Mathematics

Repository record dc:identifier

https://surface.syr.edu/etd/758

OAI identifier oai:identifier

oai:surface.syr.edu:etd-1759