Steklov eigenvalues for the \infty-Laplacian

  • Ireneo Peral

    Universidad Autónoma de Madrid, Spain
  • Jesús García-Azorero

    Universidad Autónoma de Madrid, Spain
  • Juan J. Manfredi

    University of Pittsburgh, United States
  • Julio D. Rossi

    Universidad de Buenos Aires, Argentina


We study the Steklov eigenvalue problem for the \infty-laplacian. To this end we consider the limit as pp \to \infty of solutions of Δpup=0-\Delta_p u_p =0 in a domain Ω\Omega with upp2up/ν=λup2u|\nabla u_p|^{p-2} \partial u_p / \partial \nu = \lambda |u|^{p-2} u on Ω\partial\Omega. We obtain a limit problem that is satisfied in the viscosity sense and a geometric characterization of the second eigenvalue.

Cite this article

Ireneo Peral, Jesús García-Azorero, Juan J. Manfredi, Julio D. Rossi, Steklov eigenvalues for the \infty-Laplacian. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 3, pp. 199–210

DOI 10.4171/RLM/463