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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

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

  • 1. L. A. Caffarelli, Interior a priori estimates for solutions of fully nonlinear equations, Ann. of Math. 130 (1989), 189-213. MR 90i:35046
  • 2. -, Elliptic second order equations, Rend. Sem. Mat. Fis. Milano 58 (1988), 253-284. MR 91h:35070
  • 3. M. G. Crandall and P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-42. MR 85g:35029
  • 4. L. C. Evans, A convergence theorem for solutions of nonlinear second-order elliptic equations, Indiana Univ. Math. J. 27 (1978), 875-887. MR 80e:35023
  • 5. -, On solving certain nonlinear partial differential equations by accretive operator methods, Israel J. Math. 36 (1980), 225-247. MR 82b:35032
  • 6. -, Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math. 35 (1982), 333-363. MR 83g:35038
  • 7. -, Classical solutions of the Hamilton-Jacobi-Bellman equation for uniformly elliptic operators, Trans. Amer. Math. Soc. 275 (1983), 245-255. MR 83m:35054
  • 8. D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, second ed., Springer-Verlag, Berlin and Heidelberg, 1983. MR 86c:35035
  • 9. H. Ishii, On uniqueness and existence of viscosity solutions of fully nonlinear second order PDE's, Comm. Pure Appl. Math. 42 (1989), 15-46. MR 89m:35070
  • 10. -, Perron's method for Hamilton-Jacobi equations, Duke Math. J. 55 (1987), 369-384. MR 89a:35053
  • 11. R. Jensen, The maximum principle for viscosity solutions of fully nonlinear second oder partial differential equations, Arch. Rational Mech. Anal. 101 (1988), 1-27. MR 89a:35038
  • 12. N. V. Krylov, Boundedly inhomogeneous elliptic and parabolic equations, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), 487-523 (Russian); English transl., Math. USSR-Izv. 20 (1983), 459-492. MR 84a:35091
  • 13. -, Boundedly inhomogeneous elliptic and parabolic equations in a domain, Izv. Akad. Nauk SSSR Ser. Mat. 47 (1983), 75-108 (Russian); English transl., Math. USSR-Izv. 24 (1984), 67-97. MR 85g:35046
  • 14. -, Nonlinear elliptic and parabolic equations of the second order, Reidel, Dordrecht, 1987. MR 88d:35005
  • 15. N. V. Krylov and M. V. Safonov, An estimate of the probability that a diffusion process hits a set of positive measure, Dokl. Akad. Nauk SSSR 245 (1979), 18-20 (Russian); English transl., Soviet Math. Dokl. 20 (1979), 253-255. MR 80b:60101
  • 16. -, A certain property of solutions of parabolic equations with measurable coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 40 (1980), 161-175 (Russian); English transl., Math. USSR-Izv. 16 (1981), 151-164. MR 83c:35059
  • 17. P.-L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi equations, Part II: Viscosity solutions and uniqueness, Comm. Partial Differential Equations 8 (1983), 1229-1276. MR 85i:49043b

Review Information:

Reviewer: John Urbas
Affiliation: University of Bonn
Email: urbas@math.uni-bonn.de
Journal: Bull. Amer. Math. Soc. 34 (1997), 187-191
MSC (1991): Primary 35J60; Secondary 35B65, 35D10
DOI: https://doi.org/10.1090/S0273-0979-97-00704-0
Review copyright: © Copyright 1997 American Mathematical Society
American Mathematical Society