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Asymptotic first boundary value problem for elliptic operators
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 65 / Issue 3 / September 2022
- Published online by Cambridge University Press:
- 16 July 2021, pp. 571-581
- Print publication:
- September 2022
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- Article
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In 1955, Lehto showed that, for every measurable function
$\psi $
on the unit circle 
$\mathbb T,$
there is a function f holomorphic in the unit disc, having 
$\psi $
as radial limit a.e. on 
$\mathbb T.$
We consider an analogous problem for solutions f of homogenous elliptic equations 
$Pf=0$
and, in particular, for holomorphic functions on Riemann surfaces and harmonic functions on Riemannian manifolds.
