The “hot Spots” Conjecture for Nearly Circular Planar Convex Domains
نویسنده
چکیده
We prove the “hot spots” conjecture of J. Rauch in the case that the domain Ω is a planar convex domain satisfying diam(Ω)2/|Ω| < 1.378. Specifically, we show that an eigenfunction corresponding to the lowest nonzero eigenvalue of the Neumann Laplacian on Ω attains its maximum (minimum) at points on ∂Ω. When Ω is a disk, diam(Ω)2/|Ω| t 1.273. Hence, the above condition indicates that Ω is a nearly circular planar convex domain. However, symmetries of the domain are not assumed.
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تاریخ انتشار 2007