equation of the fixed membrane in the n-dimensional space: some remarks on the maxima of the eigenfunctions subjected to various norms
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ID: 161463
1979
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Abstract
We show in this paper that the sequence {max|uk|}, where the uk are the eigenfunctions of the problem Δu+λu=0 in D⊂Rn and u=0 on ∂D, is not bounded generally if one imposes the norm ∫Du2p(x)dx=1, p=(1),2,3,…. The same holds with the norm ∫D|gradu|2pdx=1 when n>4p−1. On the other hand, if D⊂R2, resp. R3 the norm ∫D|gradu|2dx=1 implies max|uk|→k→∞0, resp. max|uk|=0(1).
| Reference Key |
biollay1979internationalequation
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|---|---|
| Authors | ;Yves Biollay |
| Journal | structural engineering and mechanics |
| Year | 1979 |
| DOI |
10.1155/S0161171279000296
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