On Neumann Eigenfunctions in Lip Domains
نویسندگان
چکیده
A planar set D will be called a lip domain if it is Lipschitz, open, bounded, connected, and given by (1) D = {(x1, x2) : f1(x1) < x2 < f2(x1)}, where f1, f2 are Lipschitz functions with constant 1. The assumption that D is a Lipschitz domain puts an extra constraint on the functions fk; we discuss this issue in greater detail later in this section. Let μ2 denote the second eigenvalue for the Laplacian inD with Neumann boundary conditions. Here is our main result.
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تاریخ انتشار 2004