A Surgery Result for the Spectrum of the Dirichlet Laplacian
نویسندگان
چکیده
In this paper we give a method to geometrically modify an open set such that the first k eigenvalues of the Dirichlet Laplacian and its perimeter are not increasing, its measure remains constant, and both perimeter and diameter decrease below a certain threshold. The key point of the analysis relies on the properties of the shape subsolutions for the torsion energy.
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عنوان ژورنال:
- SIAM J. Math. Analysis
دوره 47 شماره
صفحات -
تاریخ انتشار 2015