The first initial-boundary value problem for quasilinear second order parabolic equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 13 (1986) no. 3, p. 347-387
@article{ASNSP_1986_4_13_3_347_0,
author = {Lieberman, Gary M.},
title = {The first initial-boundary value problem for quasilinear second order parabolic equations},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 13},
number = {3},
year = {1986},
pages = {347-387},
zbl = {0655.35047},
mrnumber = {881097},
language = {en},
url = {http://www.numdam.org/item/ASNSP_1986_4_13_3_347_0}
}

Lieberman, Gary M. The first initial-boundary value problem for quasilinear second order parabolic equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 13 (1986) no. 3, pp. 347-387. http://www.numdam.org/item/ASNSP_1986_4_13_3_347_0/

[1] S. Bernstein, Sur les équations du calcul des variations, Ann. Scuola Norm Sup. Pisa, Cl. Sci., 29 (1912), pp. 431-485. | JFM 43.0460.01 | Numdam | MR 1509153

[2] D. Edmunds - L. Peletier, Quasilinear parabolic equations, Ann. Scuola Norm. Sup. Pisa, Cl. Sci., (3) 25 (1971), pp. 399-421. | Numdam | MR 306704 | Zbl 0219.35054

[3] A. Friedman, Partial differential equations of parabolic type, Krieger Press Malabar, Florida, 1983.

[4] Futev, to appear.

[5] M. Giaquinta - E. Giusti, Global C1,α-regularity for second order quasilinear elliptic equations in divergence form, J. Reine Angew. Math., 351 (1984), pp. 55-65. | Zbl 0528.35014

[6] D. Gilbarg, Boundary value problems for nonlinear elliptic equations in n variables, in: Nonlinear Problems, pp. 151-159, University of Wisconsin Press, Madison, Wisconsin, 1963. | MR 146506 | Zbl 0121.08401

[7] D. Gilbarg - L. Hörmander, Intermediate Schauder estimates, Arch. Rational Mech. Anal., 74 (1980), pp. 297-318. | MR 588031 | Zbl 0454.35022

[8] D. Gilbarg - N.S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Springer-Verlag, Berlin -Heidelberg-New York- Tokyo, 1983. | MR 737190 | Zbl 0562.35001

[9] E. Giusti, Boundary behavior of nonparametric minimal surface, Indiana Univ. Math. J., 22 (1975), pp. 435-444. | MR 305253 | Zbl 0262.35020

[10] M. Gruber, Harnack inequalities for solution of general second order parabolic equations and estimates of their Hölder constants, Math. Z., 185 (1984), pp. 23-43. | MR 724044 | Zbl 0509.35044

[11] M. Iannelli - G. Vergara Caffarelli, On the boundary value problem for surfaces of prescribed mean curvature, Sympos. Math., 14 (1974), pp. 473-480. | MR 388220 | Zbl 0307.35044

[12] A.V. Ivanov, The first boundary value problem for second order quasi-linear parabolic equations, Zap. Nauchn. Sem. Leningrad, Otdel Mat. Inst. Steklov.(LOMI), 38 (1973), pp. 10-32 [Russian]. English translation in J. Soviet Math., 8 (1977), pp. 354-372. | MR 374677 | Zbl 0404.35054

[13] A.V. Ivanov, Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order, Trudy Mat. Inst. Steklov., 160 (1982), pp. 1-285 [Russian]. English translation, Proc. Math. Inst. Steklov, 160 (1984), pp. 1-287. | MR 702172 | Zbl 0544.35003

[14] H. Jenkins - J. Serrin, The Dirichlet problem for the minimal surface equation in higher dimensions, J. Reine Angew. Math., 229 (1968), pp. 170-187. | MR 222467 | Zbl 0159.40204

[15] N.V. Krylov, On the maximum principle for nonlinear parabolic and elliptic equations, Izv. Akad. Nauk SSSR, 42 (1978), pp. 1050-1062 [Russian]. English translation in Math. USSR Izv., 13 (1979), pp. 335-347. | MR 513913 | Zbl 0421.35041

[16] N.V. Krylov, Boundedly inhomogencous elliptic and parabolic equations in a domain, Izv. Akad. Nauk SSSR, 47 (1983), pp. 75-108 [Russian]. English translation in Math. USSR Izv., 22 (1984), pp. 67-98. | MR 688919 | Zbl 0578.35024

[17] N.V. Krylov, On estimates for the derivatives of solutions of nonlinear parabolic equations, Dokl. Akad. Nauk SSSR, 274 (1984), pp. 23-26 [Russian]. English translation in Soviet Math. Dokl., 29 (1984), pp. 14-17. | MR 730158 | Zbl 0598.35057

[18] O.A. Ladyzhenskaya - N.N. Ural'Tseva, Linear and quasilinear elliptic solutions, Izd. Nauka, Moscow, 1964 [Russian]. English translation, Academic Press, New York, 1968; 2nd Russian ed., 1973.

[19] O.A. Ladyzhenskaja - V.A. Solonnikov - N.N. Ural'Tseva, Linear and quasilinear equations of parabolic type, Izd. Nauka, Moscow, 1967 [Russian]. English translation, Amer. Math. Soc., Providence, R.I., 1968. | MR 241822 | Zbl 0174.15403

[20] A. Lichnewsky - R. Temam, Pseudosolutions of the time-dependent minima surface problem, J. Differential Equations, 30 (1978), pp. 340-364. | MR 521858 | Zbl 0368.49016

[21] G.M. Lieberman, The quasilinear Dirichlet problem with decreased regularity at the boundary, Comm. Partial Differential Equations, 6 (1981), pp. 437-497. | MR 612553 | Zbl 0458.35039

[22] G.M. Lieberman, Interior gradient estimates for nonuniformly parabolic equations, Indiana Univ. Math. J., 32 (1983), pp. 579-601. | MR 703286 | Zbl 0491.35021

[23] G.M. Lieberman, Regularized distance and its applications, Pacific J. Math., 117 (1985), pp. 329-352. | MR 779924 | Zbl 0535.35028

[23] G.M. Lieberman, Intermediate Schauder theory for second order parabolic equations. I: Estimates, J. Differential Equations, to appear. | MR 840590 | Zbl 0553.35038

[25] G.M. Lieberman, Intermediate Schauder theory for second order parabolic equations. II: Existence, uniqueness and regularity, J. Differential Equations, to appear. | MR 840591 | Zbl 0553.35038

[26] G.M. Lieberman, The Dirichlet problem for quasilinear elliptic equations with continuously differentiable boundary data, to appear. | MR 818099 | Zbl 0589.35036

[27] G.M. Lieberman - N.S. Trudinger, Nonlinear oblique boundary value problems for nonlinear elliptic equations, to appear. | MR 833695 | Zbl 0619.35047

[28] P. Marcellini - K. Miller, Asymptotic growth for the parabolic equations of prescribed mean curvature, J. Differential Equations, 51 (1984), pp. 326-358. | MR 735204 | Zbl 0545.35044

[29] J. Serrin, The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables, Philos. Trans. Roy. Soc. London Ser. A, 264 (1969), pp. 413-495. | MR 282058 | Zbl 0181.38003

[30] J. Serrin, Gradient estimates for solutions of nonlinear elliptic and parabolic equations, in: Contributions to Nonlinear Functional Analysis, pp. 565-501, Academic Press, New York, 1971. | MR 402274 | Zbl 0271.35004

[31] L. Simon, Interior gradient bounds for nonuniformly elliptic equations, Indiana Univ. Math. J., 25 (1976), pp. 821-855. | MR 412605 | Zbl 0346.35016

[32] N.S. Trudinger, Pointwise estimates and quasilinear parabolic equations, Comm. Pure Appl. Math., 21 (1968), pp. 205-226. | MR 226168 | Zbl 0159.39303

[33] N.S. Trudinger, The boundary gradient estimate for quasilinear elliptic and parabolic differential equations, Indiana Univ. Math. J., 21 (1972), pp. 657-670. | MR 289942 | Zbl 0236.35022

[34] N.S. Trudinger, Fully nonlinear uniformly elliptic equations under natural structure conditions, Trans. Amer. Math. Soc., 278 (1983), pp. 751-769. | MR 701522 | Zbl 0518.35036