| The p-Laplacian operator p>1is an important operator in analysisand has a nice practical background．This thesis is for calculating theeigenvalues and eigenfunctions of theoperator by the minimax algorithm. We focus our computation onthe case that p is far away from2, i.e., p to1or p to infty.Botheigenvalues and eigenfunctions of the p-Laplacian operatorwith Dirichlet boundary condition on non-convex domain and withNeumann boundary condition will be calculated. Since the decreasingefficiency of the original minimax algorithm will be affected whenp goes away from2, we suggest an optimization procedure toimprove the decreasing efficiency of the minimax algorithm, In this way,the computing efficiency of the minimax algorithm will also beincreased．In addition, since the theoretical study on eigen problemof the p-Laplacian operator on non-convex domain is very difficult, wehope that we could find some interesting phenomenadirectly from our numerical computation results to provide someinformation for further theoretical study. |
