Approximation of Ground State Eigenvalues and Eigenfunctions of Dirichlet Laplacians |
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Authors: | Pang M M H |
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Institution: | Department of Mathematics, University of Missouri Columbia, MO 65211, USA |
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Abstract: | Let be a bounded connected open set in RN, N 2, and let 0be the Dirichlet Laplacian defined in L2(). Let > 0 be thesmallest eigenvalue of , and let > 0 be its correspondingeigenfunction, normalized by ||||2 = 1. For sufficiently small>0 we let R() be a connected open subset of satisfying
Let 0 be the Dirichlet Laplacian on R(), and let >0and >0 be its ground state eigenvalue and ground state eigenfunction,respectively, normalized by ||||2=1. For functions f definedon , we let Sf denote the restriction of f to R(). For functionsg defined on R(), we let Tg be the extension of g to satisfying
1991 Mathematics SubjectClassification 47F05. |
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Keywords: | |
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