Degree Type

Dissertation

Date of Award

2012

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Gary M. Lieberman

Abstract

Using ideas from the theory of Orlicz spaces, we discuss the Holder regularity of a bounded weak solution of a p-Laplacian type parabolic partial differential equation under generalized structure conditions. To show the Holder continuity of such solutions, we use the idea of spreading positivity and geometric characters besides the standard De Giorgi's iteration method. For showing Holder continuity of the gradient, we follow the perturbation argument. Under the generalized structure conditions, we give a uniform method of proof in an intrinsically scaled cylinder without separating degenerate and singular cases.

DOI

https://doi.org/10.31274/etd-180810-1605

Copyright Owner

Sukjung Hwang

Language

en

File Format

application/pdf

File Size

120 pages

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