Book Review

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Book Information:

Authors: Luis A. Caffarelli and Xavier Cabré

Title: Fully nonlinear elliptic equations

Additional book information: Amer. Math. Soc. Colloq. Publ., vol. 43, Amer. Math. Soc., Providence, RI, 1995, vi + 104 pp., ISBN 0-8218-0437-5, $39.00$

*Interior a priori estimates for solutions of fully nonlinear equations*, Ann. of Math. (2)

**130**(1989), no. 1, 189–213. MR

**1005611**, DOI 10.2307/1971480

*Elliptic second order equations*, Rend. Sem. Mat. Fis. Milano

**58**(1988), 253–284 (1990). MR

**1069735**, DOI 10.1007/BF02925245

*Viscosity solutions of Hamilton-Jacobi equations*, Trans. Amer. Math. Soc.

**277**(1983), no. 1, 1–42. MR

**690039**, DOI 10.1090/S0002-9947-1983-0690039-8

*A convergence theorem for solutions of nonlinear second-order elliptic equations*, Indiana Univ. Math. J.

**27**(1978), no. 5, 875–887. MR

**503721**, DOI 10.1512/iumj.1978.27.27059

*On solving certain nonlinear partial differential equations by accretive operator methods*, Israel J. Math.

**36**(1980), no. 3-4, 225–247. MR

**597451**, DOI 10.1007/BF02762047

*Classical solutions of fully nonlinear, convex, second-order elliptic equations*, Comm. Pure Appl. Math.

**35**(1982), no. 3, 333–363. MR

**649348**, DOI 10.1002/cpa.3160350303

*Classical solutions of the Hamilton-Jacobi-Bellman equation for uniformly elliptic operators*, Trans. Amer. Math. Soc.

**275**(1983), no. 1, 245–255. MR

**678347**, DOI 10.1090/S0002-9947-1983-0678347-8

*Elliptic partial differential equations of second order*, 2nd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR

**737190**, DOI 10.1007/978-3-642-61798-0

*On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDEs*, Comm. Pure Appl. Math.

**42**(1989), no. 1, 15–45. MR

**973743**, DOI 10.1002/cpa.3160420103

*Perron’s method for Hamilton-Jacobi equations*, Duke Math. J.

**55**(1987), no. 2, 369–384. MR

**894587**, DOI 10.1215/S0012-7094-87-05521-9

*The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations*, Arch. Rational Mech. Anal.

**101**(1988), no. 1, 1–27. MR

**920674**, DOI 10.1007/BF00281780

*Boundedly inhomogeneous elliptic and parabolic equations*, Izv. Akad. Nauk SSSR Ser. Mat.

**46**(1982), no. 3, 487–523, 670 (Russian). MR

**661144**

*Boundedly inhomogeneous elliptic and parabolic equations in a domain*, Izv. Akad. Nauk SSSR Ser. Mat.

**47**(1983), no. 1, 75–108 (Russian). MR

**688919**

*Nonlinear elliptic and parabolic equations of the second order*, Mathematics and its Applications (Soviet Series), vol. 7, D. Reidel Publishing Co., Dordrecht, 1987. Translated from the Russian by P. L. Buzytsky [P. L. Buzytskiĭ]. MR

**901759**, DOI 10.1007/978-94-010-9557-0

*An estimate for the probability of a diffusion process hitting a set of positive measure*, Dokl. Akad. Nauk SSSR

**245**(1979), no. 1, 18–20 (Russian). MR

**525227**

*A property of the solutions of parabolic equations with measurable coefficients*, Izv. Akad. Nauk SSSR Ser. Mat.

**44**(1980), no. 1, 161–175, 239 (Russian). MR

**563790**

*Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. I. The dynamic programming principle and applications*, Comm. Partial Differential Equations

**8**(1983), no. 10, 1101–1174. MR

**709164**, DOI 10.1080/03605308308820297

Review Information:

Reviewer: John Urbas

Affiliation: University of Bonn

Email: urbas@math.uni-bonn.de

Journal: Bull. Amer. Math. Soc.

**34**(1997), 187-191

DOI: https://doi.org/10.1090/S0273-0979-97-00704-0

Review copyright: © Copyright 1997 American Mathematical Society