Boundary relative extremal functions
Ibrahim K. Djire, Jan Wiegerinck
TL;DR
This paper explores alternative definitions of boundary relative extremal functions and demonstrates that Edwards' theorem is not valid in open sets, challenging existing assumptions in the field.
Contribution
It introduces new definitions for boundary relative extremal functions and proves the failure of Edwards' theorem in open sets, providing insights into potential limitations of current theories.
Findings
Alternative definitions of boundary relative extremal functions proposed
Edwards' theorem does not hold in open sets
Highlights limitations of existing extremal function theories
Abstract
We give alternative definitions of the boundary relative extremal function and show that Edwards' theorem does not hold in open sets.
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Taxonomy
TopicsAnalytic and geometric function theory · Nonlinear Partial Differential Equations · Geometry and complex manifolds