EXTERIOR REGULARIZED HARMONIC AND HARMONIC FUNCTIONS

This thesis mainly studies harmonic functions on exterior regions, having compact, Lipschitz boundaries, in our new finite energy function space, via the sequence of exterior harmonic Steklov eigenvalues and associated eigenfunctions. The new space is strictly larger than the standard Sobolev-Hilbert H-space, as it only needs square integrability of the gradients of the functions involved. Our results generalize exactly certain well-known results on Laplace's spherical harmonics in classical mathematical physics.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Houston

Year dc:date.issued

2012

Author dc:creator

• Han, Qi 1980-

Advisor dc:contributor.advisor

• Auchmuty, Giles

Committee members dc:contributor.committeemember

• Gorb, Yuliya
• Onofrei, Daniel
• Zhou, Jianxin

• Harmonic functions
• Exterior regions
• Finite energy space
• Steklov eigenvalue problems

Statement dc:rights

• The author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/10657/395

OAI identifier oai:identifier

oai:uh-ir.tdl.org:10657/395