%0 Journal Article
%T Equation of the fixed membrane in the n-dimensional space: some remarks on the maxima of the eigenfunctions subjected to various norms
%A Yves Biollay
%J International Journal of Mathematics and Mathematical Sciences
%D 1979
%I Hindawi Publishing Corporation
%R 10.1155/s0161171279000296
%X We show in this paper that the sequence {max|uk|}, where the uk are the eigenfunctions of the problem    ¡±u+    u=0 in D ¡é    Rn and u=0 on  ¡é    D, is not bounded generally if one imposes the norm  ¡é    Du2p(x)dx=1, p=(1),2,3, ¡é ? |. The same holds with the norm  ¡é    D|gradu|2pdx=1 when n>4p ¡é   ¡¯1. On the other hand, if D ¡é    R2, resp. R3 the norm  ¡é    D|gradu|2dx=1 implies max|uk| ¡é   ¡¯k ¡é   ¡¯ ¡é    0, resp. max|uk|=0(1).
%K elliptic equations
%K eigenvalue problems
%K eigenfuntions.
%U http://dx.doi.org/10.1155/S0161171279000296