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 ![{Delta}](http://blms.oxfordjournals.org/math/Delta.gif) ![{Omega}](http://blms.oxfordjournals.org/math/Omega.gif) 0be the Dirichlet Laplacian defined in L2( ). Let ![{lambda}](http://blms.oxfordjournals.org/math/lambda.gif) > 0 be thesmallest eigenvalue of ![{Delta}](http://blms.oxfordjournals.org/math/Delta.gif) , and let ![{varphi}](http://blms.oxfordjournals.org/math/phiv.gif) > 0 be its correspondingeigenfunction, normalized by ||![{varphi}](http://blms.oxfordjournals.org/math/phiv.gif) ||2 = 1. For sufficiently small >0 we let R( ) be a connected open subset of satisfying
Let ![{Delta}](http://blms.oxfordjournals.org/math/Delta.gif) 0 be the Dirichlet Laplacian on R( ), and let ![{lambda}](http://blms.oxfordjournals.org/math/lambda.gif) >0and ![{varphi}](http://blms.oxfordjournals.org/math/phiv.gif) >0 be its ground state eigenvalue and ground state eigenfunction,respectively, normalized by ||![{varphi}](http://blms.oxfordjournals.org/math/phiv.gif) ||2=1. For functions f definedon , we let S f denote the restriction of f to R( ). For functionsg defined on R( ), we let T g be the extension of g to satisfying
1991 Mathematics SubjectClassification 47F05. |
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