We study the Steklov eigenvalue problem for the -laplacian. To this end we consider the limit as of solutions of in a domain with on . We obtain a limit problem that is satisfied in the viscosity sense and a geometric characterization of the second eigenvalue.
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Ireneo Peral, Jesús García-Azorero, Juan J. Manfredi, Julio D. Rossi, Steklov eigenvalues for the -Laplacian. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 3, pp. 199–210DOI 10.4171/RLM/463