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Extremal solutions of \(\Delta u = Pu\). (English) Zbl 0218.31002

MSC:

31C12 Potential theory on Riemannian manifolds and other spaces
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
31A35 Connections of harmonic functions with differential equations in two dimensions
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References:

[1] BERGMAN, S., AND M. SCHIFFER, Kernel functions and elliptic differential equa-tions. Academic Press (1953), 432pp. · Zbl 0053.39003
[2] I, S., Fundamental solutions of parabolic differential equations and boundar value problems. Japan J. Math. 27 (1957), 55-102. · Zbl 0092.31101
[3] KAWAI, K., AND L. SARIO, Extremal properties of quasiharmomc forms and func tions, (to appear).
[4] NAKAI, M., Principal function problems on harmonic spaces. Sgaku 21 (1969), 254-263
[5] OZAWA, M., Classification of Riemann surfaces. Kodai Math. Sem. Rep. 4 (1952), 63-76 · Zbl 0048.31803
[6] PROTTER, M., AND H. WEINBERGER, Maximum principles in differential equations Prentice-Hall (1967), 261 pp. · Zbl 0153.13602
[7] RODIN, B., AND L. SARIO, Principal functions. Van Nostrand (1968), 347pp · Zbl 0159.10701
[8] SARIO, L., AND M. NAKAI, Classification theory of Riemann surfaces. Springe (1970), 446 pp. · Zbl 0199.40603
[9] SARIO, L., M. SCHIFFER, AND M. GLASNER, The span and principal functions i Riemannian spaces. J. Anal. Math. 15 (1965), 115-134. · Zbl 0136.09603
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