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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


MathSciNet review: 1568134
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: \break T.~Kilpel\"ainen J.~Heinonen, and O.~Martio
Title: Nonlinear potential theory of degenerate elliptic equations
Additional book information: Oxford University Press, London, 1993, v+363 pp., US$70.00. ISBN 0-19-853669-0.

References [Enhancements On Off] (What's this?)

  • Heinz Bauer, Harmonische Räume und ihre Potentialtheorie, Lecture Notes in Mathematics, No. 22, Springer-Verlag, Berlin-New York, 1966 (German). Ausarbeitung einer im Sommersemester 1965 an der Universität Hamburg gehaltenen Vorlesung. MR 0210916
  • M. Brelot, Familles de Perron et problème de Dirichlet, Acta Litt. Sci. Szeged 9 (1939), 133–153 (French). MR 734
  • M. Brelot, Lectures on potential theory, Lectures on Mathematics, vol. 19, Tata Institute of Fundamental Research, Bombay, 1960. Notes by K. N. Gowrisankaran and M. K. Venkatesha Murthy. MR 0118980
    • [4]
    -, Sur le potentiel et les suites de fonctions sous-harmoniques, C. R. Acad. Sci. Paris Ser. I. Math. 207 (1938), 836-839.
    [5]
    R. Caccioppoli, Sui teoremi d'esistenza di Riemann, Rend. Reale Accad. Sci. Fis. Mat. Napoli 4 (1934), 49-54.
  • Gianfranco Cimmino, Sulle equazioni lineari alle derivate parziali del secondo ordine di tipo ellittico sopra una superficie chiusa, Ann. Scuola Norm. Super. Pisa Cl. Sci. (2) 7 (1938), no. 1, 73–96 (Italian). MR 1556798
  • Corneliu Constantinescu and Aurel Cornea, Potential theory on harmonic spaces, Die Grundlehren der mathematischen Wissenschaften, Band 158, Springer-Verlag, New York-Heidelberg, 1972. With a preface by H. Bauer. MR 0419799
  • Ennio De Giorgi, Sulla differenziabilità e l’analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. (3) 3 (1957), 25–43 (Italian). MR 0093649
  • J. L. Doob, Classical potential theory and its probabilistic counterpart, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 262, Springer-Verlag, New York, 1984. MR 731258, DOI 10.1007/978-1-4612-5208-5
  • Nicolaas du Plessis, An introduction to potential theory, University Mathematical Monographs, No. 7, Hafner Publishing Co., Darien, Conn.; Oliver and Boyd, Edinburgh, 1970. MR 0435422
  • Alexandre Eremenko and John L. Lewis, Uniform limits of certain $A$-harmonic functions with applications to quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I Math. 16 (1991), no. 2, 361–375. MR 1139803, DOI 10.5186/aasfm.1991.1609
  • Eugene B. Fabes, Carlos E. Kenig, and Raul P. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations 7 (1982), no. 1, 77–116. MR 643158, DOI 10.1080/03605308208820218
  • Bent Fuglede, Finely harmonic functions, Lecture Notes in Mathematics, Vol. 289, Springer-Verlag, Berlin-New York, 1972. MR 0450590
  • F. W. Gehring, The $L^{p}$-integrability of the partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973), 265–277. MR 402038, DOI 10.1007/BF02392268
  • L. L. Helms, Introduction to potential theory, Pure and Applied Mathematics, Vol. XXII, Wiley-Interscience [A division of John Wiley & Sons, Inc.], New York-London-Sydney, 1969. MR 0261018
  • Peter W. Jones, A geometric localization theorem, Adv. in Math. 46 (1982), no. 1, 71–79. MR 676987, DOI 10.1016/0001-8708(82)90054-8
    • [17]
    O. D. Kellogg, Foundations of potential theory, Dover, New York, 1954.
  • T. Kilpeläinen, Potential theory for supersolutions of degenerate elliptic equations, Indiana Univ. Math. J. 38 (1989), no. 2, 253–275. MR 997383, DOI 10.1512/iumj.1989.38.38013
  • Tero Kilpeläinen and Jan Malý, The Wiener test and potential estimates for quasilinear elliptic equations, Acta Math. 172 (1994), no. 1, 137–161. MR 1264000, DOI 10.1007/BF02392793
  • N. S. Landkof, Foundations of modern potential theory, Die Grundlehren der mathematischen Wissenschaften, Band 180, Springer-Verlag, New York-Heidelberg, 1972. Translated from the Russian by A. P. Doohovskoy. MR 0350027
  • P. Lindqvist and O. Martio, Two theorems of N. Wiener for solutions of quasilinear elliptic equations, Acta Math. 155 (1985), no. 3-4, 153–171. MR 806413, DOI 10.1007/BF02392541
  • W. Littman, G. Stampacchia, and H. F. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 17 (1963), 43–77. MR 161019
    • [23]
    V. G Maz'ya, On the continuity at a boundary point of solutions of quasilinear elliptic equations, Vestnik Leningrad Univ. Math. 3 (1976), 225-242.
  • Jürgen Moser, On Harnack’s theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577–591. MR 159138, DOI 10.1002/cpa.3160140329
  • J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931–954. MR 100158, DOI 10.2307/2372841
  • Oskar Perron, Eine neue Behandlung der ersten Randwertaufgabe für $\Delta u=0$, Math. Z. 18 (1923), no. 1, 42–54 (German). MR 1544619, DOI 10.1007/BF01192395
  • Seppo Rickman, The analogue of Picard’s theorem for quasiregular mappings in dimension three, Acta Math. 154 (1985), no. 3-4, 195–242. MR 781587, DOI 10.1007/BF02392472
  • Frédéric Riesz, Sur les Fonctions Subharmoniques et Leur Rapport à la Théorie du Potentiel, Acta Math. 48 (1926), no. 3-4, 329–343 (French). MR 1555229, DOI 10.1007/BF02565338
  • James Serrin, Local behavior of solutions of quasi-linear equations, Acta Math. 111 (1964), 247–302. MR 170096, DOI 10.1007/BF02391014
    • [30]
    S. L. Sobolev, On a theorem in functional analysis, Mat. Sb. 46 (1938), 471-497. (Russian)
  • M. Tsuji, Potential theory in modern function theory, Maruzen Co. Ltd., Tokyo, 1959. MR 0114894
  • Hermann Weyl, The method of orthogonal projection in potential theory, Duke Math. J. 7 (1940), 411–444. MR 3331
    • [33]
    N. Wiener, Certain notions in potential theory, J. Math. Phys. Mass. Inst. Tech. 3 (1924), 24-51.
    [34]
    -, The Dirichlet problem, J. Math. Phys. Mass. Inst. Tech. 3 (1924), 127-146.
    [35]
    -, Note on a paper by O. Perron, J. Math. Phys. Mass. Inst. Tech. 4 (1925), 21-32.
  • V. A. Zorič, M. A. Lavrent′ev’s theorem on quasiconformal space maps, Mat. Sb. (N.S.) 74 (116) (1967), 417–433 (Russian). MR 0223569
    • Review Information:

    Reviewer: Nicola Garofalo
    Journal: Bull. Amer. Math. Soc. 31 (1994), 318-327
    DOI: https://doi.org/10.1090/S0273-0979-1994-00543-9