An axiomatic treatment of pairs of elliptic differential equations

Peter Loeb

Annales de l'institut Fourier (1966)

  • Volume: 16, Issue: 2, page 167-208
  • ISSN: 0373-0956

How to cite


Loeb, Peter. "An axiomatic treatment of pairs of elliptic differential equations." Annales de l'institut Fourier 16.2 (1966): 167-208. <>.

author = {Loeb, Peter},
journal = {Annales de l'institut Fourier},
keywords = {partial differential equations},
language = {eng},
number = {2},
pages = {167-208},
publisher = {Association des Annales de l'Institut Fourier},
title = {An axiomatic treatment of pairs of elliptic differential equations},
url = {},
volume = {16},
year = {1966},

AU - Loeb, Peter
TI - An axiomatic treatment of pairs of elliptic differential equations
JO - Annales de l'institut Fourier
PY - 1966
PB - Association des Annales de l'Institut Fourier
VL - 16
IS - 2
SP - 167
EP - 208
LA - eng
KW - partial differential equations
UR -
ER -


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  2. [2] N. BOBOC, C. CONSTANTINESCU and A. CORNEA, On the Dirichlet Problem in the Axiomatic Theory of Harmonic Functions, Nagoya Math. Journ., 23 (1963), 73-96. Zbl0139.06603MR29 #261
  3. [3] N. BOURBAKI, Intégration, Actualités Sci. Ind., 1175 (1952), Paris. Zbl0049.31703
  4. [4] M. BRELOT, Une Axiomatique Générale du Problème de Dirichlet dans les Espaces Localement Compacts, Séminaire de Théorie du Potentiel (dirigé par M. Brelot et G. Choquet), 1957, 6-01-6-16. 
  5. [5] M. BRELOT, Axiomatique des Fonctions Harmoniques et Surharmoniques dans un Espace Localement Compact, Séminaire de Théorie du Potentiel (dirigé par M. Brelot, G. Choquet et J. Deny), 1958, 1-01-1-40. 
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  7. [7] C. CONSTANTINESCU and A. CORNEA, On the Axiomatic of Harmonic Functions I, Ann. Inst. Fourier, 13,2 (1963), 373-388. Zbl0122.34001MR29 #2416
  8. [8] R. COURANT and D. HILBERT, Methods of Mathematical Physics, Inter-science Publishers, New York, 1962. Zbl0099.29504
  9. [9] K. GOWRISANKARAN, Extreme Harmonic Functions and Boundary Value Problems, Ann. Inst. Fourier, 13,2 (1963), 307-356. Zbl0134.09503MR29 #1350
  10. [10] R.-M. HERVÉ, Recherches Axiomatiques sur la Théorie des Fonctions Surharmoniques et du Potentiel, Ann. Inst. Fourier, Grenoble, 12 (1962), 415-571. Zbl0101.08103MR25 #3186
  11. [11] K. HOFFMAN, Banach Spaces of Analytic Functions, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962. Zbl0117.34001MR24 #A2844
  12. [12] O. PERRON, Eine Neue Behandlung der Ersten Randwertaufgabe für ∆u = 0, Math. Z., 18 (1923), 42-54. JFM49.0340.01
  13. [13] H. L. ROYDEN, The Equation ∆u = Pu, and the Classification of Open Riemann Surfaces, Mathematica, Helsinki, 271 (1959). Zbl0096.05803MR22 #12215
  14. [14] H. L. ROYDEN, Real Analysis, Macmillan, New York, 1963. Zbl0121.05501MR27 #1540

Citations in EuDML Documents

  1. Sadoon Ibrahim Othman, Victor Anandam, Biharmonic Green domains in a Riemannian manifold
  2. Peter Loeb, Bertram Walsh, A maximal regular boundary for solutions of elliptic differential equations
  3. Eva Čermáková, The insertion of regular sets in potential theory
  4. John C. Taylor, On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold
  5. Victor Anandam, Espaces harmoniques sans potentiel positif
  6. John C. Taylor, The Martin boundaries of equivalent sheaves
  7. Bertram Walsh, Flux in axiomatic potential theory. II. Duality
  8. Linda Lumer-Naïm, p -spaces of harmonic functions

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