On definitions of superharmonic functions

Seizô Itô

Annales de l'institut Fourier (1975)

  • Volume: 25, Issue: 3-4, page 309-316
  • ISSN: 0373-0956

Abstract

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Let A be an elliptic differential operator of second order with variable coefficients. In this paper it is proved that any A -superharmonic function in the Riesz-Brelot sense is locally summable and satisfies the A -superharmonicity in the sense of Schwartz distribution.

How to cite

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Itô, Seizô. "On definitions of superharmonic functions." Annales de l'institut Fourier 25.3-4 (1975): 309-316. <http://eudml.org/doc/74249>.

@article{Itô1975,
abstract = {Let $A$ be an elliptic differential operator of second order with variable coefficients. In this paper it is proved that any $A$-superharmonic function in the Riesz-Brelot sense is locally summable and satisfies the $A$-superharmonicity in the sense of Schwartz distribution.},
author = {Itô, Seizô},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3-4},
pages = {309-316},
publisher = {Association des Annales de l'Institut Fourier},
title = {On definitions of superharmonic functions},
url = {http://eudml.org/doc/74249},
volume = {25},
year = {1975},
}

TY - JOUR
AU - Itô, Seizô
TI - On definitions of superharmonic functions
JO - Annales de l'institut Fourier
PY - 1975
PB - Association des Annales de l'Institut Fourier
VL - 25
IS - 3-4
SP - 309
EP - 316
AB - Let $A$ be an elliptic differential operator of second order with variable coefficients. In this paper it is proved that any $A$-superharmonic function in the Riesz-Brelot sense is locally summable and satisfies the $A$-superharmonicity in the sense of Schwartz distribution.
LA - eng
UR - http://eudml.org/doc/74249
ER -

References

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  1. [1] M. BRELOT, Éléments de la théorie classique du potentiel, Centre Doc. Univ. Paris, 3e éd. 1956. Zbl0098.07001
  2. [2] S. ITÔ, Fundamental solutions of parabolic differential equations and boundary value problems, Japan. J. Math., 27 (1957), 55-102. Zbl0092.31101MR20 #4702
  3. [3] F. RIESZ, Sur les fonctions subharmoniques et leur rapport à la théorie du potentiel, Acta Math., 48 (1926), 329-343 ; 54 (1930), 321-360. Zbl52.0497.05JFM52.0497.05
  4. [4] L. SCHWARTZ, Théorie des distributions, Hermann, Paris, 1966. 

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