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arXiv · 1104.5211

Separately twice differentiable functions and the equation of string oscillation

Taras Banakh·Volodymyr Mykhaylyuk
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Abstract

We prove that for every separately twice differentiable solution $f$ of the PDE $f"_{xx}=f"_{yy}$ is of the form $f(x,y)=\phi(x+y)+\psi(x-y)$ for some twice differentiable functions $\phi, \psi$.

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Taras Banakh, Volodymyr Mykhaylyuk. 2011-04-27. Separately twice differentiable functions and the equation of string oscillation. https://arxiv.org/abs/1104.5211

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