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MODULUS OF CONTINUITY OF THE DIRICHLET SOLUTIONS

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84093

Title: MODULUS OF CONTINUITY OF THE DIRICHLET SOLUTIONS
Authors: Aikawa, Hiroaki Browse this author
Keywords: Modulus of continuity
Dirichlet solution
concave function
Issue Date: 30-Sep-2009
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 946
Start Page: 1
End Page: 11
Abstract: Let 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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69753
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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