Complex analysis texts typically discuss analytic functions whose real and imaginary components are harmonic and satisfy the Laplace equation, $\nabla^2 f = 0$.

I am working with a complex function whose real and imaginary components satisfy the biharmonic equation instead, i.e. $\nabla^4 f= 0$. Thus far I have not been able to find very many resources and was wondering if anyone could point me towards any good books or papers covering this topic.

  • $\begingroup$ Perhaps you would like to have a look at arxiv.org/pdf/math/0510636.pdf. Surely you already know that a biharmonic function is the real part of $\overline zf(z)+g(z)$ for some holomorphic functions $f$ and $g$. $\endgroup$
    – John B
    Feb 29, 2016 at 15:35
  • $\begingroup$ @Jonas Thanks, I will take a look at it. $\endgroup$
    – Ragnar
    Feb 29, 2016 at 19:33


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