|
Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Retrieve article in:
PDF
Book Information
Author(s):
J.~Heinonen, T.~Kilpel\"ainen, 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:
- [1]
- H. Bauer, Harmonische R\"aume und ihre Potentialtheorie, Lecture Notes in Math., vol. 22, Springer-Verlag, Berlin, 1966.
- [\brea ]
- M. Brelot , Familles de Perron et probl\`eme de Dirichlet, Acta Sci. Math. (Szeged) \textbf{{IX}} (1939), 133--153.
- [3]
- , Lectures on potential theory, Tata Inst. Fund. Res. Lectures on Math. and Phys., no. 19, Tata Inst. Fund. Res., Bombay, 1960.
- [4]
- , Sur le potentiel et les suites de fonctions sous-harmoniques, C. R. Acad. Sci. Paris Ser. I. Math. \textbf{207} (1938), 836--839.
- [5]
- R. Caccioppoli, Sui teoremi d'esistenza di Riemann, Rend. Reale Accad. Sci. Fis. Mat. Napoli \textbf{4} (1934), 49--54.
- [6]
- G. Cimmino, Sulle equazioni lineari alle derivate parziali del secondo ordine di tipo ellittico sopra una superficie chiusa, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) \textbf{7} (1938), 73--96.
- [7]
- C. Costantinescu and A. Cornea, Potential theory of harmonic spaces, Springer-Verlag, Berlin, 1972.
- [8]
- E. De Giorgi, Sulla differenziabilit\`a e l'analiticit\`a delle estremali degli integrali multipli regolari, Mem. Reale Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. \textbf{3} (1957), 25--43.
- [9]
- J. L. Doob, Classical potential theory and its probabilistic counterpart, Grundlehren Math. Wiss., vol. 262, Springer-Verlag, New York, 1984.
- [10]
- N. Du Plessis, An introduction to potential theory, Oliver and Boyd, Edinburgh, 1970.
- [11]
- A. Eremenko and J. L. Lewis, Uniform limits of certain $\sA $-harmonic functions with applications to quasiregular mappings, Ann. Acad. Sci. Fenn., Ser. A I. Math. \textbf{16} (1991), 361--375.
- [12]
- E. B. Fabes, C. E. Kenig, and R. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations \textbf{7} (1982), 77--116.
- [13]
- B. Fuglede, Finely harmonic functions, Lecture Notes in Math., vol. 289, Springer-Verlag, Berlin, 1972.
- [14]
- F. Gehring, The $L^p$-integrability of the partial derivatives of quasiconformal mappings, Acta Math. \textbf{130} (1973), 265--277.
- [15]
- L. L. Helms, Introduction to potential theory, Wiley-Interscience, New York, 1969.
- [16]
- D. S. Jerison and C. E. Kenig, Boundary behavior of harmonic functions in nontangentially accessible domains, Adv. Math. \textbf{46} (1982), 80--147.
- [17]
- O. D. Kellogg, Foundations of potential theory, Dover, New York, 1954.
- [18]
- T. Kilpel\"ainen, Potential theory for supersolutions of degenerate elliptic equations, Indiana Univ. Math. J. \textbf{38} (1989), 253--275.
- [19]
- T. Kilpel\"ainen and J. Mal\'y, The Wiener test and potential estimates for quasilinear elliptic equations, Acta Math. \textbf{172} (1994), 137--161.
- [20]
- N. S. Landkof, Foundations of modern potential theory, Springer-Verlag, Berlin, 1972.
- [21]
- P. Lindqvist and O. Martio, Two theorems of N. Wiener for solutions of quasilinear elliptic equations, Acta Math. \textbf{155} (1985), 153--171.
- [22]
- W. Littman, G. Stampacchia, and H. F. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) \textbf{17} (1963), 43--77.
- [23]
- V. G. Maz'ya, On the continuity at a boundary point of solutions of quasilinear elliptic equations, Vestnik Leningrad Univ. Math. \textbf{3} (1976), 225--242.
- [24]
- J. Moser, On Harnack\RM 's theorem for elliptic differential equations, Comm. Pure Appl. Math. \textbf{14} (1961), 577--591.
- [25]
- J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. \textbf{80} (1958), 931--954.
- [26]
- O. Perron, Eine neue Behandlung der ersten Randwertaufgabe fur $\D u=0$, Math. Z. \textbf{18} (1923), 42--54.
- [27]
- S. Rickman, The analogue of Picard\RM 's theorem for quasiregular mappings in dimension three, Acta Math. \textbf{154} (1985), 195--242.
- [28]
- F. Riesz, Sur les fonctions subharmoniques et leur rapport \`a la th\'eorie du potentiel. \RM I, Acta Math. \textbf{48} (1926), 329--343.
- [29]
- J. Serrin, Local behavior of solutions of quasilinear equations, Acta Math. \textbf{111} (1964), 247--302.
- [30]
- S. L. Sobolev, On a theorem in functional analysis, Mat. Sb. \textbf{46} (1938), 471--497. (Russian)
- [31]
- M. Tsuji, Potential theory in modern function theory, Maruzen Co. Ltd., Tokyo, 1959.
- [32]
- H. Weyl, The method of orthogonal projection in potential theory, Duke Math. J. \textbf{7} (1940), 411--444.
- [\weia ]
- N. Wiener , Certain notions in potential theory, J. Math. Phys. Mass. Inst. Tech. \textbf{3} (1924), 24--51.
- [34]
- , The Dirichlet problem, J. Math. Phys. Mass. Inst. Tech. \textbf{3} (1924), 127--146.
- [35]
- , Note on a paper by O. Perron, J. Math. Phys. Mass. Inst. Tech. \textbf{4} (1925), 21--32.
- [36]
- V. A. Zorich, The theorem of M. A. Lavrent\cprime {}ev on quasiconformal mappings in space, Mat. Sb. \textbf{74} (1967), 417--433.
Additional Information:
Reviewer(s):
Nicola
Garofalo
Review Information:
Journal:
Bull. Amer. Math. Soc.
31
(1994),
318-327.
DOI:
10.1090/S0273-0979-1994-00543-9
PII:
S 0273-0979(1994)00543-9
|
Comments: webmaster@ams.org