Displaying similar documents to “Behavior of invariant metrics near convexifiable boundary points”

Trivial generators for nontrivial fibres

Linus Carlsson (2008)

Mathematica Bohemica

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Pseudoconvex domains are exhausted in such a way that we keep a part of the boundary fixed in all the domains of the exhaustion. This is used to solve a problem concerning whether the generators for the ideal of either the holomorphic functions continuous up to the boundary or the bounded holomorphic functions, vanishing at a point in ℂ n where the fibre is nontrivial, has to exceed n . This is shown not to be the case.

Nonuniqueness for some linear oblique derivative problems for elliptic equations

Gary M. Lieberman (1999)

Commentationes Mathematicae Universitatis Carolinae

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It is well-known that the “standard” oblique derivative problem, Δ u = 0 in Ω , ∂ u / ∂ ν - u = 0 on ∂ Ω ( ν is the unit inner normal) has a unique solution even when the boundary condition is not assumed to hold on the entire boundary. When the boundary condition is modified to satisfy an obliqueness condition, the behavior at a single boundary point can change the uniqueness result. We give two simple examples to demonstrate what can happen.