ISOLATION AND SIMPLICITY FOR THE FIRST EIGENVALUE OF THE p-LAPLACIAN WITH A NONLINEAR BOUNDARY CONDITION
نویسنده
چکیده
Here Ω is a bounded domain in RN with smooth boundary, ∆pu = div(|∇u|p−2∇u) is the p-Laplacian, and ∂/∂ν is the outer normal derivative. In the linear case, that is for p = 2, this eigenvalue problem is known as the Steklov problem (see [3]). Problems of the form (1.1) appear in a natural way when one considers the Sobolev trace inequality. In fact, the immersionW1,p(Ω) ↪→ Lp(∂Ω) is compact, hence there exists a constant λ1 such that
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Eigenvalues of the Laplace operator with nonlinear boundary conditions ∗
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