Isolation and simplicity for the first eigenvalue of the $p$-Laplacian with a nonlinear boundary condition

By S. Martínez, Julio D. Rossi. 2002

88 citations recorded by the source corpus.

We prove the simplicity and isolation of the first eigenvalue for the problem Δpu=|u|p−2u in a bounded smooth domain Ω⊂ℝN, with a nonlinear boundary condition given by |∇u|p−2∂u/∂v=λ|u|p−2u on the boundary of the domain.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7f9d62fc41e14a8cab7acfe378a3dcdf0e1e80eb

Citations in the corpus

• Uniqueness (2021, unknown): “Again it is standard to show that A is not empty (contains a global minimizer of I ). is simple; see [62] for an alternative proof based on arguments from [58, Appendix] on the strict convexity of the function Example 4.9 ( p -Laplacian Allen-Cahn problems) .”