Electron. J. Diff. Eqns.,
Vol. 2006(2006), No. 111, pp. 19.
On the first eigenvalue of the Steklov eigenvalue problem for the
infinity Laplacian
An Le
Abstract:
Let
be the best Sobolev embedding constant of
,
where
is a smooth bounded domain in
.
We prove that as
the sequence
converges to a constant independent of the shape
and the volume of
,
namely 1.
Moreover, for any sequence of eigenfunctions
(associated with
),
normalized by
,
there is a subsequence converging to a limit function
which satisfies, in the viscosity sense, an
Laplacian
equation with a boundary condition.
Submitted August 4, 2006. Published September 18, 2006.
Math Subject Classifications: 35J50, 35J55, 35J60, 35J65, 35P30.
Key Words: Nonlinear elliptic equations; eigenvalue problems;
pLaplacian; nonlinear boundary condition;
Steklov problem; viscosity solutions.
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An Lê
Department of Mathematics and Statistics
Utah State University
Logan, Utah 84322, USA
email: anle@cc.usu.edu 
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