An axiomatic treatment of pairs of elliptic differential equations. (English) Zbl 0172.15101

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[1] H. BAUER, Axiomatische behandlung des dirichletschen problems für elliptische und parabolische differentialgleichungen, Math. Annalen, 146 (1962), 1-59. · Zbl 0107.08003
[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. · Zbl 0139.06603
[3] N. BOURBAKI, Intégration, Actualités Sci. Ind., 1175 (1952), Paris. · Zbl 0049.31703
[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] 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.
[6] M. BRELOT, Lectures on potentiel theory, Tata Institute of Fundamental Research, Bombay, (1960). · Zbl 0098.06903
[7] C. CONSTANTINESCU and A. CORNEA, On the axiomatic of harmonic functions I, Ann. Inst. Fourier, 13,2 (1963), 373-388. · Zbl 0122.34001
[8] R. COURANT and D. HILBERT, Methods of mathematical physics, Inter-science Publishers, New York, 1962. · Zbl 0099.29504
[9] K. GOWRISANKARAN, Extreme harmonic functions and boundary value problems, Ann. Inst. Fourier, 13,2 (1963), 307-356. · Zbl 0134.09503
[10] R.-M. HERVÉ, Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier, Grenoble, 12 (1962), 415-571. · Zbl 0101.08103
[11] K. HOFFMAN, Banach spaces of analytic functions, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962. · Zbl 0117.34001
[12] O. PERRON, Eine neue behandlung der ersten randwertaufgabe für ∆u = 0, math. Z., 18 (1923), 42-54. · JFM 49.0340.01
[13] H. L. ROYDEN, The equation ∆u = pu, and the classification of open Riemann surfaces, Mathematica, Helsinki, 271 (1959). · Zbl 0096.05803
[14] H. L. ROYDEN, Real analysis, Macmillan, New York, 1963. · Zbl 0121.05501
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