The p-Laplacian Problem via an Euler Equation and the Basis Properties of Its Eigenfunctions
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 Lr((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.
Suarez Salas, Luis R, "The p-Laplacian Problem via an Euler Equation and the Basis Properties of Its Eigenfunctions" (2018). ETD Collection for University of Texas, El Paso. AAI10823081.