XII: 26, 378-397, LNM 649 (1978)
BROSSARD, Jean
Comportement non-tangentiel et comportement brownien des fonctions harmoniques dans un demi-espace. Démonstration probabiliste d'un théorème de Calderon et Stein (Potential theory, Real analysis)
Given a harmonic function $u$ in a half space, Stein (Acta Math. 106, 1961) shows that the boundary points $x$ such that 1) $u$ has a non-tangential limit at $x$, 2) $u$ is ``non tangentially bounded'' near $x$, 3) $\nabla u$ is locally $L^2$ in the non-tangential cones at $x$, are the sames, except for sets of measure $0$. This result is given here a probabilistic proof using conditional Brownian motion
Keywords: Harmonic functions in a half-space, Non-tangential limits
Nature: Original
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