= Dirichlet eigenfunction supremum estimate
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{title2=$\|u\|_\infty\leq C(n)\lambda^{n/4}\|u\|_2$}
For $n\geq3$ and a bounded smooth domain, a <Dirichlet Laplacian eigenfunction> with <eigenvalue> $\lambda$ satisfies the displayed estimate. A <signed power test for a Laplacian eigenfunction> and the zero-boundary <Sobolev inequality> give a <Moser iteration> with exponents $p_j=2[n/(n-2)]^j$. The <geometric series> $\sum_j1/p_j=n/4$ gives the exact power of $\lambda$, while $\sum_j(\log p_j)/p_j<\infty$ controls the remaining constant. The constant depends only on dimension, because the zero-boundary <Sobolev inequality> follows by extension by zero to the whole space.
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