Separately twice differentiable functions and the equation of string oscillation

Details Separately twice differentiable functions and the equation of string oscillation Separately twice differentiable functions and the equation of string oscillation

2011-04-27

arxiv.org/abs/1104.5211v1

Mathematics

Analysis of PDEs

17 pages

Scientific paper

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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