Advanced search
Publication Cover
Complex Variables and Elliptic Equations
An International Journal
Volume 60, 2015 - Issue 12
Submit an article Journal homepage
110
Views
3
CrossRef citations to date
0
Altmetric
Articles

Another version of Kellogg’s theorem

S.B. KlimentovSouthern Mathematical Institute of VSC RAS, Southern Federal University, Rostov-on-Don, Russian Federation.Correspondence[email protected]
Pages 1647-1657 | Received 18 Oct 2014, Accepted 02 Apr 2015, Published online: 05 May 2015

References

  • Vekua IN. Generalized analytic functions. Moscow: Fizmatgiz; 1959. Russian. English translation: Vekua IN. Generalized analytic functions. Oxford: Pergamon Press; 1962. XXIX + 668 S.
  • Agmon S, Douglis A, Nirenberg L. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Comm Pure Appl. Math. 1959;XII:623–727.
  • Monakhov VN. Boundary-value problems with free boundaries for elliptic systems of equations. Vol. 57, Translations of mathematical monographs. Providence (RI): American Mathematcal Society; 1983.
  • Kellogg OD. Potential functions on the boundary on their regions of definition. Trans. Amer. Math. Soc. 1908;9:39–50.
  • Kellogg OD. Harmonic functions and Green’s integral. Trans. Amer. Math. Soc. 1912;13:109–132.
  • Warschawski S. Über das Randverhalten der Abbildungsfunktion bei konformer Abbildung [About boundary behavior of conformal mapping]. Math Zeitschr. 1932;35:321–456.
  • Warschawski SE. On the higher derivatives at the boundary in conformal mappings. Trans. Amer. Math. Soc. 1935;38:310–340.
  • Goluzin GM. Geometrical theory of functions of complex variable. Vol. 26, Translations of mathematical monographs. Providence (RI): American Mathematical Society; 1969.
  • Krantz SG. Geometric function theory. Explorations in complex analysis. Boston: Birkhäuser; 2006.
  • Klimentov SB. Representations of the for the Hardy classes of solutions to the Beltrami equation. Siberian Math. J. 2014;55:262–275.
  • Klimentov SB. Analogue of Kellogg’s theorem to the generalized Beltrami equation. Izv Vuz Sev Kav Region. Estestv nauki. 2013;6:27–29. Russian.
  • Bojarski B. Generalized solutions of a system of differential equations of first order and of elliptic type with discontinuous coefficients. Mat. Sb. 1957;43:451–503. Russian. English translation in Rep. Univ. Jyväskylä Dept. Math. Stat. 2009;118.
  • Campanato S. Elliptic systems in divergence form, interior regularity. Pisa: Quaderni, Scuola Normale Superiore; 1980.
  • Muskhelishvili NI. Singular integral equations. Moscow: Nauka; 1968. Russian.
  • Stein EM. Singular integrals and differentiability properties of functions. Princeton (NJ): Princeton University Press; 1970.
  • Kudryavtsev LD. About properties of harmonic mappings of the plane domains. Mat. Sb. 1955;36:201–208. Russian.
  • Miranda K. Partial differential equations of the elliptic type. Moscow: Izdatinlit; 1957. Russian.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.