Monotonicity of the principal eigenvalue of the 𝑝-Laplacian in an annulus

Monotonicity of the principal eigenvalue of the $p$-Laplacian in an annulus
HTML articles powered by AMS MathViewer

by B. Emamizadeh and M. Zivari-Rezapour PDF

Proc. Amer. Math. Soc. 136 (2008), 1725-1731 Request permission

In this note we prove a monotonicity result related to the principal eigenvalue of the $p$-Laplacian in an annulus in $\mathbb {R}^N$.

References

Lucio Damascelli, Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results, Ann. Inst. H. Poincaré C Anal. Non Linéaire 15 (1998), no. 4, 493–516 (English, with English and French summaries). MR 1632933, DOI 10.1016/S0294-1449(98)80032-2
Mitsuharu Ôtani and Toshiaki Teshima, On the first eigenvalue of some quasilinear elliptic equations, Proc. Japan Acad. Ser. A Math. Sci. 64 (1988), no. 1, 8–10. MR 953752
A. G. Ramm and P. N. Shivakumar, Inequalities for the minimal eigenvalue of the Laplacian in an annulus, Math. Inequal. Appl. 1 (1998), no. 4, 559–563. MR 1646670, DOI 10.7153/mia-01-54
J. Simon, Differentiation with respect to the domain in boundary value problems, Numer. Funct. Anal. Optim. 2 (1980), no. 7-8, 649–687 (1981). MR 619172, DOI 10.1080/01630563.1980.10120631