Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the derivatives of harmonic functions on the boundary
HTML articles powered by AMS MathViewer

by Oliver D. Kellogg PDF
Trans. Amer. Math. Soc. 33 (1931), 486-510 Request permission

Abstract:

Let U be harmonic in a closed region R, whose boundary contains a regular surface element E, with a representation $z = \phi (x,y)$. If E has bounded curvatures, and if $\phi (x,y)$ and the boundary values of U on E have continuous derivatives of order n which satisfy a Dini condition, then the partial derivatives of U of order n exist, as limits, on E, and are continuous in R at any interior point of E. Hölder conditions on the boundary values of U, or on their derivatives of order n, imply Hölder conditions on U, or the corresponding derivatives, in R, in the neighborhood of the interior points of E.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 31A05
  • Retrieve articles in all journals with MSC: 31A05
Additional Information
  • © Copyright 1931 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 33 (1931), 486-510
  • MSC: Primary 31A05
  • DOI: https://doi.org/10.1090/S0002-9947-1931-1501602-2
  • MathSciNet review: 1501602