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On the maximum principle for harmonic functions
Author(s):
A.
Vagharshakyan
Original publication:
Algebra i Analiz,
tom 20
(2008),
nomer 3.
Journal:
St. Petersburg Math. J.
20
(2009),
325-337.
MSC (2000):
Primary 30C80, 31A15
Posted:
April 6, 2009
MathSciNet review:
2454450
Retrieve article in:
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Additional information
Abstract:
Some generalizations of the maximum principle for harmonic functions are discussed.
References:
-
- 1.
- S. Mandelbrojt, Séries de Dirichlet. Principes et méthodes, Monogr. Internat. Math. Modernes, vol. 11, Gauthier-Villars, Paris, 1969. MR 0259079 (41:3721)
- 2.
- L. Carleson, Selected problems on exceptional sets, Van Nostrand Math. Stud., No. 13, Van Nostrand Co., Inc., Princeton, NJ, 1967. MR 0225986 (37:1576)
- 3.
- E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Math. Ser., No. 30, Princeton Univ. Press, Princeton, NJ, 1970. MR 0290095 (44:7280)
- 4.
- A. Vagarshakyan, On the maximum principle, Izv. Akad. Nauk Armenii Mat. 26 (1991), no. 4, 300-308 (1992); English transl., Contemp. Math. Anal. 26 (1991), no. 4, 21-28. MR 1231851 (94h:30031)
- 5.
- -, Boundary properties of certain classes of harmonic functions, Izv. Akad. Nauk Armyan. SSR Ser. Mat. 10 (1975), no. 1, 54-60. (Russian) MR 0382681 (52:3563)
- 6.
- Henrik Shahgholian and Ashot Vagharshakyan, On Phragmen Lindelöf principle, Complex Variables Theory Appl. 46 (2001), no. 4, 295-305. MR 1873963 (2002j:30032)
- 7.
- L. Hörmander, The analysis of linear partial differential operators. I, Grundlehren Math. Wiss., Bd. 256, Springer-Verlag, Berlin, 1983. MR 0717035 (85g:35002a)
- 8.
- N. Landkof, Foundations of modern potential theory, ``Nauka'', Moscow, 1966; English transl., Grundlehren Math. Wiss., Bd. 180, Springer-Verlag, New York-Heidelberg, 1972. MR 0214795 (35:5644); MR 0350027 (50:2520)
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Additional Information:
A.
Vagharshakyan
Affiliation:
Institute of Mathematics, Armenian National Academy of Sciences, Bagramian 24-b, 375019, Yerevan, Armenia
Email:
vagharshakyan@yahoo.com
DOI:
10.1090/S1061-0022-09-01050-4
PII:
S 1061-0022(09)01050-4
Keywords:
Harmonic functions,
maximum principle
Received by editor(s):
5/MAR/2007
Posted:
April 6, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
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