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- W2257974974 abstract "Let $uleft( t,yright) $ be a polyharmonic function of order $N$ defined on the strip $left( a,bright) timesmathbb{R}^{d}$ satisfying the growth condition $$ sup_{tin K}leftvert uleft( t,yright) rightvert leq oleft( leftvert yrightvert ^{left( 1-dright) /2}e^{frac{pi}{c}leftvert yrightvert }right) $$ for $leftvert yrightvert rightarrowinfty$ and any compact subinterval $K$ of $left( a,bright) $, and suppose that $uleft( t,yright) $ vanishes on $2N-1$ equidistant hyperplanes of the form $left{ t_{j}right} timesmathbb{R}^{d}$ for $t_{j}=t_{0}+jcinleft( a,bright) $ and $j=-left( N-1right) ,...,N-1.$ Then it is shown that $uleft( t,yright) $ is odd at $t_{0},$ i.e. that $uleft( t_{0}+t,yright) =-uleft( t_{0}-t,yright) $ for $yinmathbb{R}^{d}$. The second main result states that $u$ is identically zero provided that $u$ satisfies the growth condition and vanishes on $2N$ equidistant hyperplanes with distance $c.$" @default.
- W2257974974 created "2016-06-24" @default.
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- W2257974974 date "2015-10-08" @default.
- W2257974974 modified "2023-09-27" @default.
- W2257974974 title "A symmetry property for polyharmonic functions vanishing on equidistant hyperplanes" @default.
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