Uniform bound on the eigenfunctions of the Laplacian - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T15:57:33Z http://mathoverflow.net/feeds/question/118692 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/118692/uniform-bound-on-the-eigenfunctions-of-the-laplacian Uniform bound on the eigenfunctions of the Laplacian John Zheng 2013-01-12T01:27:18Z 2013-01-12T01:27:18Z <p>Hi all,</p> <p>Is it possibly to have $L_\infty$ bounds on the eigenfunctions of the Laplacian operator on bounded regular domains with Dirichlet condition? I found several papers by Sogge but these are pretty general and apply to Laplacian-Beltrami operator on manifolds. Their paper has bounds that are possibly too loose for my application.</p> <p>Thanks, John</p>