Date Available
4-23-2014
Year of Publication
2014
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
Mathematics
First Advisor
Dr. John Lewis
Abstract
We study the Hausdorff dimension of a certain Borel measure associated to a positive weak solution of a certain quasilinear elliptic partial differential equation in a simply connected domain in the plane. We also assume that the solution vanishes on the boundary of the domain. Then it is shown that the Hausdorff dimension of this measure is less than one, equal to one, greater than one depending on the homogeneity of the certain function. This work generalizes the work of Makarov when the partial differential equation is the usual Laplace's equation and the work of Lewis and his coauthors when it is the p-Laplace's equation.
Recommended Citation
Akman, Murat, "On the Dimension of a Certain Measure Arising from a Quasilinear Elliptic Partial Differential Equation" (2014). Theses and Dissertations--Mathematics. 12.
https://uknowledge.uky.edu/math_etds/12
