Book Review
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MathSciNet review:
1568010
Full text of review:
PDF
This review is available free of charge.
Book Information:
Author:
Guangchang Dong
Title:
Nonlinear partial differential equations of second order
Additional book information:
Transl. Math. Monographs, Amer. Math. Soc., Providence, RI, 1991, vii\,+\,249 pp., US$136.00. ISBN 0-8218-4554-3.
Emmanuele DiBenedetto, Continuity of weak solutions to a general porous medium equation, Indiana Univ. Math. J. 32 (1983), no. 1, 83–118. MR 684758, DOI 10.1512/iumj.1983.32.32008
E. DiBenedetto, On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 13 (1986), no. 3, 487–535. MR 881103
Emmanuele DiBenedetto and Avner Friedman, Hölder estimates for nonlinear degenerate parabolic systems, J. Reine Angew. Math. 357 (1985), 1–22. MR 783531, DOI 10.1515/crll.1985.357.1
A. V. Ivanov, Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order, Proc. Steklov Inst. Math. 1(160) (1984), xi+287. A translation of Trudy Mat. Inst. Steklov 160 (1982); Translated from the Russian by J. R. Schulenberger. MR 753230
N. V. Krylov, Nelineĭnye èllipticheskie i parabolicheskie uravneniya vtorogo poryadka, “Nauka”, Moscow, 1985 (Russian). MR 815513
O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural′ceva, Lineĭ nye i kvazilineĭ nye uravneniya parabolicheskogo tipa, Izdat. “Nauka”, Moscow, 1967 (Russian). MR 0241821
Gary M. Lieberman, Interior gradient bounds for nonuniformly parabolic equations, Indiana Univ. Math. J. 32 (1983), no. 4, 579–601. MR 703286, DOI 10.1512/iumj.1983.32.32041
Gary M. Lieberman, The first initial-boundary value problem for quasilinear second order parabolic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 13 (1986), no. 3, 347–387. MR 881097
Paul E. Sacks, Continuity of solutions of a singular parabolic equation, Nonlinear Anal. 7 (1983), no. 4, 387–409. MR 696738, DOI 10.1016/0362-546X(83)90092-5
- [1]
- E. DiBenedetto, Continuity of weak solutions to a general porous medium equation, Indiana Univ. Math. J. 32 (1983), 83-118. MR 684758 (85c:35010)
- [2]
- -, On the local behavior of solutions of degenerate parabolic equations with measurable coefficients, Ann. Norm. Sup. Pisa 13 (1986), 487-535. MR 881103 (89a:35118)
- [3]
- E. DiBenedetto and A. Friedman, HÖlder estimates for nonlinear degenerate parabolic systems, J. Reine Angew. Math. 357 (1985), 1-22. MR 783531 (87f:35134a)
- [4]
- A. V. Ivanov, Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order, Trudy Mat. Inst. Steklov. 160 (1982), 1-285; English transl., Proc. Steklov Inst. Math. 160 (1984), 1-287. MR 753230 (85e:35055)
- [5]
- N. V. Krylov, Nonlinear elliptic and parabolic equations of second order, "Nauka", Moscow, 1985; English transl., Reidel, Dodrecht, 1987. MR 815513 (87h:35002)
- [6]
- O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural´ ceva, Linear and quasilinear equations of parabolic type, "Nauka", Moscow, 1967; English transl., Amer. Math. Soc., Providence, RI, 1968. MR 0241822 (39:3159b)
- [7]
- G. M. Lieberman, Interior gradient bounds for non-uniformly parabolic equations, Indiana Univ. Math. J. 32 (1983), 579-601. MR 703286 (85i:35079)
- [8]
- -, The first initial-boundary value problem for quasilinear second order parabolic equations, Ann. Scuola Norm. Sup. Pisa 13 (1986), 347-387. MR 881097 (88e:35108)
- [9]
- P. E. Sacks, Continuity of solutions of a singular parabolic equation, Nonlinear Anal. 7 (1983), 387-409. MR 696738 (84d:35081)
Review Information:
Reviewer:
Gary M. Lieberman
Journal:
Bull. Amer. Math. Soc.
28 (1993), 161-164
DOI:
https://doi.org/10.1090/S0273-0979-1993-00342-2
