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Completeness and existence of bounded biharmonic functions on a riemannian manifold

Leo Sario (1974)

Annales de l'institut Fourier

A.S. Galbraith has communicated to us the following intriguing problem: does the completeness of a manifold imply, or is it implied by, the emptiness of the class H 2 B of bounded nonharmonic biharmonic functions? Among all manifolds considered thus far in biharmonic classification theory (cf. Bibliography), those that are complete fail to carry H 2 B -functions, and one might suspect that this is always the case. We shall show, however, that there do exist complete manifolds of any dimension that carry...

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.

Currently displaying 121 – 140 of 700