2023-03-28T07:45:00Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/697532022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116MODULUS OF CONTINUITY OF THE DIRICHLET SOLUTIONSAikawa, HiroakiModulus of continuityDirichlet solutionconcave function410Let D be a bounded domain in Rn with n >= 2. For a function f on ∂D we denote by HDf the Dirichlet solution of f over D. It is classical that if D is regular, then HD maps the family of continuous boundary functions to the family of harmonic functions in D continuous up to the boundary ∂D. We show that the better continuity of a boundary function f ensures the better continuity of HDf in the context of general modulus of continuity.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69753info:doi/10.14943/84093https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69753/1/pre946.pdfHokkaido University Preprint Series in Mathematics9461112009-09-30engpublisher