A fine limit property of functions superharmonic outside a manifold
The Dirichlet problem with non-compact boundary.
Angular Limits of Holomorphic Functions Which Satisfy an Integrability Condition.
Maximum principles for subharmonic functions.
Convexity and subharmonicity.
Superharmonic extension and harmonic approximation
Let be an open set in and be a subset of . We characterize those pairs which permit the extension of superharmonic functions from to , or the approximation of functions on by harmonic functions on .
Universal Taylor series, conformal mappings and boundary behaviour
A holomorphic function on a simply connected domain is said to possess a universal Taylor series about a point in if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta outside (provided only that has connected complement). This paper shows that this property is not conformally invariant, and, in the case where is the unit disc, that such functions have extreme angular boundary behaviour.
Smooth potentials with prescribed boundary behaviour.
This paper examines when it is possible to find a smooth potential on a C1 domain D with prescribed normal derivatives at the boundary. It is shown that this is always possible when D is a Liapunov-Dini domain, and this restriction on D is essential. An application concerning C1 superharmonic extension is given.
On a conjecture of Král concerning the subharmonic extension of continuously differentiable functions
This note verifies a conjecture of Král, that a continuously differentiable function, which is subharmonic outside its critical set, is subharmonic everywhere.
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