World Scientific Pub Co Pte Ltd
A condition equivalent to the Hölder continuity of harmonic functions on unbounded Lipschitz domains
Our main result concerns the behavior of bounded harmonic functions on a domain in [Formula: see text] which may be represented as a strict epigraph of a Lipschitz function on [Formula: see text]. Generally speaking, the result says that the Hölder continuity of a harmonic function on such a domain is equivalent to the uniform Hölder continuity along the straight lines determined by the vector [Formula: see text], where [Formula: see text] is the base of standard vectors in [Formula: see text]....
Preuzmite dokument
2025
Marijan Marković
