2
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0answers
85 views

First Weighted Eigenvalue of the Laplacian

Let $\Omega$ be a ball centered in the origin and let $\lambda_1(\Omega)$ be the first (or lowest) eigenvalue of the Dirichlet Laplacian in $\Omega$: $$\lambda_1 (\Omega) =\min_{u\in H_0^1 (\Omega),\ ...
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1answer
137 views

Find an upper bound for lowest eigenvalue using calculus of variations.

So I'm doing a little calculus of variations on an eigenvalue problem. The goal of this is to find an upper bound for the $\omega_0$ as follows: $\omega_0^2 \leq ...