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Applications of Choquet simplexes to elliptic and parabolic boundary value problems. (English) Zbl 0255.46018


MSC:

46E15 Banach spaces of continuous, differentiable or analytic functions
35B99 Qualitative properties of solutions to partial differential equations
35K20 Initial-boundary value problems for second-order parabolic equations
31D05 Axiomatic potential theory
35J25 Boundary value problems for second-order elliptic equations
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[1] Ahlfors, L; Sario, L, Riemann surfaces, (1960), Princeton Univ. Press Princeton, N.J · Zbl 0196.33801
[2] Alfsen, E, On the geometry of Choquet simplexes, Math. scand., 15, 97-110, (1964) · Zbl 0189.42802
[3] Asimow, L, Universally well-capped cones, Pacific J. math., 26, 421-431, (1968) · Zbl 0167.42102
[4] Bauer, H, Šilovsche rand und dirichletsches problem, Ann. inst. Fourier (Grenoble), 11, 89-136, (1961) · Zbl 0098.06902
[5] Bauer, H, Harmonische Räume und ihre potentialtheorie, () · Zbl 0142.38402
[6] Boboc, N; Cornea, A, Cônes des fonctions continues sur un espace compact, C. R. H. acad. sc., 261, 2564-2567, (1965) · Zbl 0151.19003
[7] Boboc, N; Cornea, A, Convex cones of lower semicontinuous functions, Rev. raum. math. pures appl., 12, 471-525, (1967) · Zbl 0155.17301
[8] Bony, J, Représentation intégrale sur LES cônes convexes faiblement complets, (), 5.01-5.07, 3e année
[9] Brelot, M, Sur l’approximation et la convergence dans la théorie des fonctions harmoniques ou holomorphes, Bull. soc. math. France, 73, 55-70, (1945) · Zbl 0061.22804
[10] Brelot, M, Éléments de la théorie classique du potential, (1959), C. D. U Paris · Zbl 0084.30903
[11] Brelot, M, Sur un théorème de prolongement fonctionnel de keldych concernant le problème de Dirichlet, J. analyse math., 8, 273-288, (1960/1961) · Zbl 0111.09604
[12] Brelot, M, Axiomatique des fonctions harmoniques, () · Zbl 0148.10401
[13] Choquet, G, Mesures coniques maximales sur LES cônes convexes faiblement complets, (), 12.01-12.15, 6e Année
[14] Choquet, G, Lectures on analysis, (1969), W. A. Benjamin New York
[15] Constantinescu, C, Some properties of the balayage of measures on a harmonic space, Ann. inst. Fourier, (Grenoble), 17, 273-293, (1967) · Zbl 0159.40804
[16] Davies, E.B, On the Banach duals of certain spaces with the Riesz decomposition property, Quart. J. math., 18, 399-414, (1967) · Zbl 0147.11102
[17] {\scE. B. Davies}, The structure and theory of the pre-dual of a Banach lattice, (to be published).
[18] de la Pradelle, A, Approximation et charactère de quasi-analyticité dans la théorie axiomatique des fonctions harmonique, Ann. inst. Fourier, (Grenoble), 17, 383-399, (1967) · Zbl 0153.15501
[19] Edwards, D.A, Minimum-stable wedges of semicontinuous functions, Math. scand., 19, 15-26, (1966) · Zbl 0146.37002
[20] Edwards, D.A; Vincent-Smith, G, A Weierstrass-stone theorem for Choquet simplexes, Ann. inst. Fourier, (Grenoble), 18, 261-282, (1968) · Zbl 0172.15604
[21] Effros, E, Structure in simplexes, Acta math., 117, 103-121, (1967) · Zbl 0154.14201
[22] Effros, E, Structure in simplexes II, J. funct. anal., 1, 379-391, (1967) · Zbl 0179.17302
[23] Effros, E; Gleit, A, Structure in simplexes III, Trans. amer. math. soc., 142, 355-379, (1969) · Zbl 0191.41201
[24] {\scE. Effros}, Structure in simplexes IV, (to be published).
[25] Friedman, A, Partial differential equations of parabolic type, (1964), Prentice-Hall Englewood Cliffs, N. J · Zbl 0144.34903
[26] Fuchs, L, Riesz vector spaces, () · Zbl 0139.29801
[27] Gamelin, T.W; Rossi, H, ()
[28] Garabedian, P.R, Partial differential equations, (1964), Wiley New York · Zbl 0124.30501
[29] Gevrey, M; Gevrey, M, Sur LES équations aux dérivées du type parabolique, J. math. pures appl., J. math. pures appl., 10, 105-148, (1914) · JFM 45.0571.03
[30] Halmos, P.R, Measure theory, (1950), Van Nostrand Princeton, N. J · Zbl 0117.10502
[31] Hervé, R.M, Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. inst. Fourier, (Grenoble), 12, 415-571, (1962) · Zbl 0101.08103
[32] Kadison, R.V, A representation theory for commutative topological algebras, Mem. amer. math. soc., 7, (1951) · Zbl 0042.34801
[33] Kamke, E, Über die erste randwertaufgabe bei der Laplace — und der Wärmeleitungs — differentialgleichung, J. deutschen math. verein, 62, 1-33, (1959) · Zbl 0087.30402
[34] Keldych, M.V, On the solvability and stability of the Dirichlet problem, Usp. mat. nauk USSR, 8, 171-231, (1941), (Russian)
[35] Keldych, M.V; Lavrentieff, Sur le problème de Dirichlet, C. R. H. acad. sci., 204, 1788, (1937) · JFM 63.0454.02
[36] Kelley, J.L, General topology, (1955), Van Nostrand Princeton, N. J · Zbl 0066.16604
[37] Kelley, J.L; Namioka, I, Linear topological spaces, (1963), Van Nostrand Princeton, N. J
[38] Kohn, J; Nirenberg, L, Degenerate elliptic-parabolic equations of second order, Comm. pure appl. math., 20, 797-872, (1967) · Zbl 0153.14503
[39] Köhn, J; Sieveking, M, Reguläre und extremale randpunkte in der potentialtheorie, Rev. roum. math. pures appl., 12, 1489-1502, (1967) · Zbl 0158.12804
[40] Kuratowski, C, Topologie. vol. I, Monografie matematyczne, Tom XX, (1952), Warsaw · Zbl 0049.39703
[41] Littman, W; Stampacchia, G; Weinberger, H, Regular points for elliptic equations with discontinuous coefficients, Ann. scuola. norm. sup. Pisa, 17, 45-79, (1963) · Zbl 0116.30302
[42] Loomis, L, An introduction to abstract harmonic analysis, (1953), Van Nostrand Princeton, N. J · Zbl 0052.11701
[43] Milgram, A.N, Parabolic equations, () · Zbl 0128.09302
[44] Namioka, I, Partially ordered linear topological spaces, Mem. amer. math. soc., 24, (1957) · Zbl 0105.08901
[45] Perdrizet, F, Sur certains espaces de Banach ordonnés, Bull. sci. math., 92, 129-141, (1968) · Zbl 0177.15901
[46] Petrovsky, I.G, Zur ersten randwertaufgabe der Wärmeleitungsgleichung, Compositio math., 1, 383-419, (1935) · Zbl 0010.29903
[47] Petrovsky, I.G, Partial differential equations, (1954), Interscience New York, (translated from the 1950 Russian edition) · Zbl 0059.08402
[48] Phelps, R, Lectures on Choquet’s theorem, (1966), Van Nostrand Princeton, N. J · Zbl 0135.36203
[49] Rogalski, M, Espace de Banach ordonnés, simplexes, frontières de silov, et problème de Dirichlet, C. R. H. acad. sci., 263, 726-729, (1966) · Zbl 0145.37802
[50] Smirnov, V.I, (), (translation from the 1959 Russian edition)
[51] Sternberg, W, Über die differentialgleichung der Wärmeleitung, Math. ann., 101, 394-398, (1929) · JFM 55.0290.14
[52] Tsuji, M, Potential theory in modern function theory, (1959), Maruzen Tokyo · Zbl 0087.28401
[53] {\scP. Taylor}, The structure space of a Choquet simplex, (to be published) · Zbl 0199.43603
[54] {\scA. Gleit}, thesis, Stanford University, Palo Alto, California 94305.
[55] Boboc, N; Constantinescu, C; Cornea, A, Axiomatic theory of harmonic functions. non-negative superharmonic functions, Ann, inst. Fourier, (Grenoble), 15, 283-312, (1965) · Zbl 0139.06604
[56] Rogalski, M, Opérateurs de lion, projecteurs boréliens et simplexes, C. R. H. acad. sci. Paris, 265, 563-566, (1967) · Zbl 0153.16302
[57] Rogalski, M, Opérateurs simpliciaux, structure borélienne des simplexes, simplexes analytique, C. R. H. acad. sci. Paris, 265, 610-613, (1967) · Zbl 0179.17103
[58] {\scE. Effros and J. Kazdan}, On the Dirichlet Problem for the heat Equation, J. Math. Mech., (to be published). · Zbl 0216.12702
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