Book Review
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Book Information:
Author:
Peter D. Lax
Title:
Functional analysis
Additional book information:
Wiley-Interscience,
New York,
2002,
xix+ 580 pp.,
ISBN 0-471-55604-1,
US$105.00$
Luis A. Caffarelli, Basilis Gidas, and Joel Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (1989), no. 3, 271–297. MR 982351, DOI 10.1002/cpa.3160420304
John B. Conway, A course in functional analysis, 2nd ed., Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1990. MR 1070713
David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, Springer-Verlag, Berlin, 2001. Reprint of the 1998 edition. MR 1814364
Pengfei Guan, $C^2$ a priori estimates for degenerate Monge-Ampère equations, Duke Math. J. 86 (1997), no. 2, 323–346. MR 1430436, DOI 10.1215/S0012-7094-97-08610-5
John M. Lee and Thomas H. Parker, The Yamabe problem, Bull. Amer. Math. Soc. (N.S.) 17 (1987), no. 1, 37–91. MR 888880, DOI 10.1090/S0273-0979-1987-15514-5
Louis Nirenberg, Topics in nonlinear functional analysis, Courant Lecture Notes in Mathematics, vol. 6, New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2001. Chapter 6 by E. Zehnder; Notes by R. A. Artino; Revised reprint of the 1974 original. MR 1850453, DOI 10.1090/cln/006
J. Sacks and K. Uhlenbeck, The existence of minimal immersions of $2$-spheres, Ann. of Math. (2) 113 (1981), no. 1, 1–24. MR 604040, DOI 10.2307/1971131
Michael Struwe, Variational methods, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 34, Springer-Verlag, Berlin, 2000. Applications to nonlinear partial differential equations and Hamiltonian systems. MR 1736116, DOI 10.1007/978-3-662-04194-9
M. Takesaki, Theory of operator algebras. I, Encyclopaedia of Mathematical Sciences, vol. 124, Springer-Verlag, Berlin, 2002. Reprint of the first (1979) edition; Operator Algebras and Non-commutative Geometry, 5. MR 1873025
Kôsaku Yosida, Functional analysis, 6th ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 123, Springer-Verlag, Berlin-New York, 1980. MR 617913
- 1.
- L. Caffarelli, B. Gidas and J. Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (1989), 271-297. MR 0982351
- 2.
- John B. Conway, A Course in Functional Analysis, Second edition. Graduate Texts in Mathematics, 96. Springer-Verlag, New York, 1990. MR 1070713
- 3.
- D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order. Reprint of the 1998 edition. Classics in Mathematics, Springer-Verlag, Berlin-New York, 2001. MR 1814364
- 4.
- P. Guan,
a priori estimates for degenerate Monge-Ampère equations, Duke Math. J. 86 (1997), 323-346. MR 1430436
- 5.
- J. Lee and T. Parker, The Yamabe problem, Bull. Amer. Math. Soc. (N.S.) 17 (1987), 37-91. MR 0888880
- 6.
- L. Nirenberg, Topics in Nonlinear Functional Analysis, Courant Lecture Notes in Mathematics, 6. American Mathematical Society, Providence, RI, 2001. MR 1850453
- 7.
- P. Sacks and K. Uhlenbeck, On the existence of minimal immersions of 2-spheres, Ann. of Math. 113 (1981), 1-24. MR 0604040
- 8.
- M. Struwe, Variational methods. Applications to nonlinear partial differential equations and Hamiltonian systems. Third edition. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, 34. Springer-Verlag, Berlin-New York, 2000. MR 1736116
- 9.
- M. Takesaki, Theory of operator algebras, I-III, Encyclopaedia of Mathematical Sciences, 124, 125, 127. Springer-Verlag, Berlin, 2002, 2003. MR 1873025, MR 1943006 (2004g:46079), MR 1943007
- 10.
- K. Yosida, Functional Analysis, Sixth edition. Grundlehren der Mathematischen Wissenschaften, 123. Springer-Verlag, Berlin-New York, 1980. MR 0617913
Review Information:
Reviewer:
Meijun Zhu
Affiliation:
University of Oklahoma
Email:
mzhu@math.ou.edu
Journal:
Bull. Amer. Math. Soc.
43 (2006), 123-126
Published electronically:
July 6, 2005
Review copyright:
© Copyright 2005
American Mathematical Society
