Existence and Classification of Solutions to Nonlinear Elliptic Equations

Author

Haseeb E. Ansari, The University of Texas Rio Grande Valley

Date of Award

5-2019

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. John Villavert

Second Advisor

Dr. Paul Bracken

Third Advisor

Dr. Andras Balogh

Abstract

The so-called Lane-Emden equation is a model in astrophysics, useful to problems in analysis and conformal geometry, and is closely related to the Yamabe Problem and the Uniformization Theorem. We discuss several important results for the equation, which include proving that the equation admits a distribution solution if and only if p is greater than the Serrin exponent, that classical solutions admit the form of a "bubble function" if p is equal to the Sobolev exponent, and no classical solutions exist for p less than the Sobolev exponent. A new proof of an extended result is also included.

Comments

Copyright 2019 Haseeb E. Ansari. All Rights Reserved.

https://go.openathens.net/redirector/utrgv.edu?url=https://www.proquest.com/dissertations-theses/existence-classification-solutions-nonlinear/docview/2245837256/se-2?accountid=7119

Recommended Citation

Ansari, Haseeb E., "Existence and Classification of Solutions to Nonlinear Elliptic Equations" (2019). Theses and Dissertations. 419.
https://scholarworks.utrgv.edu/etd/419