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

Hayk Mikayelyan

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arXiv · 1609.01749

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

Hayk Mikayelyan

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Abstract

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 $f=\pm u_1$.

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Hayk Mikayelyan. 2016-09-05. Short note on energy maximization property of the first eigenfunction of the Laplacian. https://arxiv.org/abs/1609.01749

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