A remark on the Dirichlet problem in a half-plane
2014 (English)In: Journal of inequalities and applications (Print), ISSN 1029-242X, E-ISSN 1029-242X, 497Article in journal (Refereed) Published
In this paper, we prove that if the positive part u(+)(z) of a harmonic function u(z) in a half-plane satisfies a slowly growing condition, then its negative part u(-)(z) can also be dominated by a similarly growing condition. Further, a solution of the Dirichlet problem in a half-plane for a fast growing continuous boundary function is constructed by the generalized Dirichlet integral with this boundary function.
Place, publisher, year, edition, pages
harmonic function, Dirichlet problem, half-plane
IdentifiersURN: urn:nbn:se:su:diva-113703DOI: 10.1186/1029-242X-2014-497ISI: 000347470400009OAI: oai:DiVA.org:su-113703DiVA: diva2:796304