Numerical investigation of the smallest eigenvalues of the p-Laplace operator on planar domains

Electronic Journal of Differential Equations

关键词: p-Laplace operator;    eigenvalue;    mountain pass algorithm;    symmetry;   

DOI  :  

来源: DOAJ

【 摘 要 】

The eigenvalue problem for the p-Laplace operator with p>1 onplanar domains with zero Dirichlet boundary condition isconsidered. The Constrained Descent Method and the ConstrainedMountain Pass Algorithm are used in the Sobolev space setting tonumerically investigate the dependence of the two smallesteigenvalues on p. Computations are conducted for values of pbetween 1.1 and 10. Symmetry properties of the second eigenfunctionare also examined numerically. While for the disk an odd symmetryabout the nodal line dividing the disk in halves is maintained forall the considered values of p, for rectangles and trianglessymmetry changes as p varies. Based on the numerical evidence thechange of symmetry in this case occurs at a certain value p_0which depends on the domain.

【 授权许可】

Unknown