Geodesic
Asymptotic first boundary value problem for elliptic operators
Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 571-581

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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.
DOI : 10.4153/S0008439521000503
Mots-clés : elliptic equations, manifolds, approximation in measure, Dirichlet problem 
Falcó, Javier; Gauthier, Paul M. Asymptotic first boundary value problem for elliptic operators. Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 571-581. doi: 10.4153/S0008439521000503
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     title = {Asymptotic first boundary value problem for elliptic operators},
     journal = {Canadian mathematical bulletin},
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     year = {2022},
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