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Convergence in nonisotropic regions of harmonic functions in n

Carme Cascante, Joaquin Ortega (1999)

Studia Mathematica

We study the boundedness in L p ( n ) of the projections onto spaces of functions with spectrum contained in horizontal strips. We obtain some results concerning convergence along nonisotropic regions of harmonic extensions of functions in L p ( n ) with spectrum included in these horizontal strips.

Convex domains and unique continuation at the boundary.

Vilhelm Adolfsson, Luis Escauriaza, Carlos Kenig (1995)

Revista Matemática Iberoamericana

We show that a harmonic function which vanishes continuously on an open set of the boundary of a convex domain cannot have a normal derivative which vanishes on a subset of positive surface measure. We also prove a similar result for caloric functions vanishing on the lateral boundary of a convex cylinder.

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