Date of Award
2018-01-01
Degree Name
Master of Science
Department
Mathematical Sciences
Advisor(s)
Osvaldo Méndez
Abstract
The Laplacian operator is used in many fields of science, such as fluidodynamics, mechanics and elasticity. Mathematically, much research has been devoted to develop a theory with which it and other variations can be understood. In this work, we present the p-Laplacian problem via an Euler equation. We then study the properties of its eigenfunctions which generalize the trigonometric functions sine and cosine. In connection with a Fourier series, we then show the generalized trigonometric functions possess basis properties for L^r((0,1)^d), d=1,2,3. Finally, we introduce the spaces of variable exponent and the analogue p(x)-Laplacian problem which has immense applications such as in image restoration and in the modeling of electrorheological fluids.
Language
en
Provenance
Received from ProQuest
Copyright Date
2018-05
File Size
62 pages
File Format
application/pdf
Rights Holder
Luis Suarez Salas
Recommended Citation
Suarez Salas, Luis, "The P-Laplacian Problem Via An Euler Equation And The Basis Properties Of Its Eigenfunctions" (2018). Open Access Theses & Dissertations. 1546.
https://scholarworks.utep.edu/open_etd/1546