article · Pacific Journal of Mathematics · 1980

The boundary modulus of continuity of harmonic functions

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Abstract

Let G be a bounded domain in the complex plane and let u(z) be continuous on G. In this paper we study the boundary modules of continuity, (), of u on dG and the modulus of continuity, (), of u on G. We investigate the extent to which the inequality "() <(<5)" holds when u is harmonic on G and show that the precise formulation of such inequalities depends on the smoothness of dG.

Cite this paper

APA 7

Johnston, E. (1980). The boundary modulus of continuity of harmonic functions. Pacific Journal of Mathematics, 90(1), 87–98. https://doi.org/10.2140/pjm.1980.90.87

MLA 9

Johnston, Elgin. “The boundary modulus of continuity of harmonic functions.” Pacific Journal of Mathematics, vol. 90, no. 1, 1980, pp. 87–98, https://doi.org/10.2140/pjm.1980.90.87.

Chicago

Johnston, Elgin. 1980. “The boundary modulus of continuity of harmonic functions.” Pacific Journal of Mathematics 90 (1): 87–98. https://doi.org/10.2140/pjm.1980.90.87.

Harvard

Johnston, E. (1980) ‘The boundary modulus of continuity of harmonic functions’, Pacific Journal of Mathematics, 90(1), pp. 87–98. Available at: https://doi.org/10.2140/pjm.1980.90.87.

BibTeX

@article{johnston1980boundary,
  title = {{The boundary modulus of continuity of harmonic functions}},
  author = {Johnston, Elgin},
  journal = {Pacific Journal of Mathematics},
  volume = {90},
  number = {1},
  pages = {87--98},
  year = {1980},
  doi = {10.2140/pjm.1980.90.87}
}

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