Radial limits of solutions to elliptic partial differential equations

For certain elliptic differential operators L, we study the behaviour of solutions to Lu=0,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Lu=0,$$\end{document} as we tend to the boundary along radii in strictly starlike domains in Rn,n >= 3.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>n, n\ge 3.$$\end{document} Analogous results are obtained in other special domains. Our approach involves introducing harmonic line bundles as instances of Brelot harmonic spaces and approximating continuous functions by harmonic functions on appropriate subsets. We are required to approximate on certain closed sets, which is not obvious, since the space of continuous functions on an (unbounded) closed set, endowed with the topology of uniform convergence, is not a topological vector space, though it is both a vector space and a topological space. Pour certaines & eacute;quations aux d & eacute;riv & eacute;es partielles, nous & eacute;tudions le comportement de solutions & agrave; Lu=0,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Lu=0,$$\end{document} lorsque nous tendons vers la fronti & eacute;re le long de rayons dans des domaines strictement & eacute;toil & eacute;s de Rn,n >= 3.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>n, n\ge 3.$$\end{document} Des r & eacute;sultats semblables sont obtenus dans d'autres domaines sp & eacute;ciaux. Notre approche inclut l'introduction de fibr & eacute;s harmoniques en droites comme exemple d'espace de Brelot et l'approximation de fonctions continues par fonctions harmoniques sur des sous-ensembles appropri & eacute;s. Nous devons faire l'approximation sur certains ensembles ferm & eacute;s, ce qui n'est pas & eacute;vident, puisque l'espace des fonctions continues sur un ensemble ferm & eacute; (non-born & eacute;), muni de la topologie de convergence uniforme, n'est pas un espace vectoriel topologique, malgr & eacute; qu'il soit & agrave; la fois un espace vectoriel et un espace topologique.