Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Application of Serrin's kernel parametrix to the uniqueness of $ L_1$ solutions of elliptic equations in the unit ball


Author: J. R. Diederich
Journal: Proc. Amer. Math. Soc. 47 (1975), 341-347
MSC: Primary 35J15
DOI: https://doi.org/10.1090/S0002-9939-1975-0355308-0
MathSciNet review: 0355308
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper it will be established that $ {L_1}$ solutions of elliptic partial differential equations, with $ \alpha $-Hölder continuous coefficients, which assume their boundary values mean continuously on the boundary of the $ N$-dimensional unit ball are uniquely determined. An additional application of the kernel will be to establish the Fatou radial limit theorem.


References [Enhancements On Off] (What's this?)

  • [1] J. R. Diederich, Representation of superharmonic functions mean continuous at the boundary of the unit ball. Pacific J. Math. (to appear). MR 0361120 (50:13566)
  • [2] L. L. Helms, Introduction to potential theory, Pure and Appl. Math., vol. 22, Wiley, New York, 1969. MR 41 #5638. MR 0261018 (41:5638)
  • [3] J. B. Serrin, Jr., On the Harnack inequality for linear elliptic equations, J. Analyse Math. 4(1955/56), 292-308. MR 18, 398. MR 0081415 (18:398f)
  • [4] V. L. Shapiro, Fourier series in several variables, Bull. Amer. Math. Soc. 70(1964), 48-93. MR 28 #1448. MR 0158222 (28:1448)
  • [5] K.-O. Widman, On the boundary behavior of solutions to a class of elliptic partial differential equations, Ark. Mat. 6 (1967), 485-533. MR 36 #2949. MR 0219875 (36:2949)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35J15

Retrieve articles in all journals with MSC: 35J15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0355308-0
Keywords: Second order elliptic, uniqueness, mean continuity, radial limit
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society