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The eigenvalue problem for the p-Laplace operator with p>1 on planar domainswith the zero Dirichlet boundary condition is considered. The ConstrainedDescent Method and the Constrained Mountain Pass Algorithm are used in theSobolev space setting to numerically investigate the dependence of the twosmallest eigenvalues on p. Computations are conducted for values of p between1.1 and 10. Symmetry properties of the second eigenfunction are also examinednumerically. While for the disk an odd symmetry about the nodal line dividingthe disk in halves is maintained for all the considered values of p, forrectangles and triangles symmetry changes as p varies. Based on the numericalevidence the change of symmetry in this case occurs at a certain value p_0which depends on the domain.

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