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arXiv:1609.01749 [math.AP]AbstractReferencesReviewsResources

Short note on energy maximization property of the first eigenfunction of the Laplacian

Hayk Mikayelyan

Published 2016-09-05Version 1

We consider the Dirichlet-energy maximization problem of the solution $u_f$ of (\ref{main}), among all functions $f\in L^2(D)$, such that $\|f\|_2= 1$. We show that the two maximizers are the first eigenfunctions of the Laplacian with Dirichlet boundary condition $f=\pm u_1$.

Categories: math.AP
Subjects: 35P15, 35P99
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