Asymptotic first boundary value problem for elliptic operators

英文摘要：

In 1955, Lehto showed that, for every measurable function $ψ$ on the unit circle $\mathbb T,$ there is a function $f$ holomorphic in the unit disc, having $ψ$ 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.