Date of Award
Master of Science
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.
Received from ProQuest
Luis Suarez Salas
Suarez Salas, Luis, "The P-Laplacian Problem Via An Euler Equation And The Basis Properties Of Its Eigenfunctions" (2018). Open Access Theses & Dissertations. 1546.