EXTERIOR REGULARIZED HARMONIC AND HARMONIC FUNCTIONS

dc.contributor.advisorAuchmuty, Giles
dc.contributor.committeeMemberGorb, Yuliya
dc.contributor.committeeMemberOnofrei, Daniel
dc.contributor.committeeMemberZhou, Jianxin
dc.creatorHan, Qi 1980-
dc.date.accessioned2013-07-16T15:43:58Z
dc.date.available2013-07-16T15:43:58Z
dc.date.createdAugust 2012
dc.date.issued2012-08
dc.date.updated2013-07-16T15:44:04Z
dc.description.abstractThis 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.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginborn digital
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/10657/395
dc.language.isoeng
dc.rightsThe 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).
dc.subjectHarmonic functions
dc.subjectExterior regions
dc.subjectFinite energy space
dc.subjectSteklov eigenvalue problems
dc.subject.lcshPartial differential equations
dc.titleEXTERIOR REGULARIZED HARMONIC AND HARMONIC FUNCTIONS
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Natural Sciences and Mathematics
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.majorPartial Differential Equations
thesis.degree.nameDoctor of Philosophy

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