@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}, pages = {347--387}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 13}, number = {3}, year = {1986}, mrnumber = {881097}, zbl = {0655.35047}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_1986_4_13_3_347_0/} }
TY - JOUR AU - Lieberman, Gary M. TI - The first initial-boundary value problem for quasilinear second order parabolic equations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1986 SP - 347 EP - 387 VL - 13 IS - 3 PB - Scuola normale superiore UR - http://archive.numdam.org/item/ASNSP_1986_4_13_3_347_0/ LA - en ID - ASNSP_1986_4_13_3_347_0 ER -
%0 Journal Article %A Lieberman, Gary M. %T The first initial-boundary value problem for quasilinear second order parabolic equations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1986 %P 347-387 %V 13 %N 3 %I Scuola normale superiore %U http://archive.numdam.org/item/ASNSP_1986_4_13_3_347_0/ %G en %F 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, Série 4, Tome 13 (1986) no. 3, pp. 347-387. http://archive.numdam.org/item/ASNSP_1986_4_13_3_347_0/
[1] Sur les équations du calcul des variations, Ann. Scuola Norm Sup. Pisa, Cl. Sci., 29 (1912), pp. 431-485. | EuDML | JFM | Numdam | MR
,[2] Quasilinear parabolic equations, Ann. Scuola Norm. Sup. Pisa, Cl. Sci., (3) 25 (1971), pp. 399-421. | EuDML | Numdam | MR | Zbl
- ,[3] Partial differential equations of parabolic type, Krieger Press Malabar, Florida, 1983.
,[4]
, to appear.[5] Global C1,α-regularity for second order quasilinear elliptic equations in divergence form, J. Reine Angew. Math., 351 (1984), pp. 55-65. | EuDML | Zbl
- ,[6] Boundary value problems for nonlinear elliptic equations in n variables, in: Nonlinear Problems, pp. 151-159, University of Wisconsin Press, Madison, Wisconsin, 1963. | MR | Zbl
,[7] Intermediate Schauder estimates, Arch. Rational Mech. Anal., 74 (1980), pp. 297-318. | MR | Zbl
- ,[8] Elliptic partial differential equations of second order, 2nd ed., Springer-Verlag, Berlin -Heidelberg-New York- Tokyo, 1983. | MR | Zbl
- ,[9] Boundary behavior of nonparametric minimal surface, Indiana Univ. Math. J., 22 (1975), pp. 435-444. | MR | Zbl
,[10] Harnack inequalities for solution of general second order parabolic equations and estimates of their Hölder constants, Math. Z., 185 (1984), pp. 23-43. | MR | Zbl
,[11] On the boundary value problem for surfaces of prescribed mean curvature, Sympos. Math., 14 (1974), pp. 473-480. | MR | Zbl
- ,[12] 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 | Zbl
,[13] 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 | Zbl
,[14] The Dirichlet problem for the minimal surface equation in higher dimensions, J. Reine Angew. Math., 229 (1968), pp. 170-187. | MR | Zbl
- ,[15] 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 | Zbl
,[16] 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 | Zbl
,[17] 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 | Zbl
,[18] Linear and quasilinear elliptic solutions, Izd. Nauka, Moscow, 1964 [Russian]. English translation, Academic Press, New York, 1968; 2nd Russian ed., 1973.
- ,[19] Linear and quasilinear equations of parabolic type, Izd. Nauka, Moscow, 1967 [Russian]. English translation, Amer. Math. Soc., Providence, R.I., 1968. | MR | Zbl
- - ,[20] Pseudosolutions of the time-dependent minima surface problem, J. Differential Equations, 30 (1978), pp. 340-364. | MR | Zbl
- ,[21] The quasilinear Dirichlet problem with decreased regularity at the boundary, Comm. Partial Differential Equations, 6 (1981), pp. 437-497. | MR | Zbl
,[22] Interior gradient estimates for nonuniformly parabolic equations, Indiana Univ. Math. J., 32 (1983), pp. 579-601. | MR | Zbl
,[23] Regularized distance and its applications, Pacific J. Math., 117 (1985), pp. 329-352. | MR | Zbl
,[23] Intermediate Schauder theory for second order parabolic equations. I: Estimates, J. Differential Equations, to appear. | MR | Zbl
,[25] Intermediate Schauder theory for second order parabolic equations. II: Existence, uniqueness and regularity, J. Differential Equations, to appear. | MR | Zbl
,[26] The Dirichlet problem for quasilinear elliptic equations with continuously differentiable boundary data, to appear. | MR | Zbl
,[27] Nonlinear oblique boundary value problems for nonlinear elliptic equations, to appear. | MR | Zbl
- ,[28] Asymptotic growth for the parabolic equations of prescribed mean curvature, J. Differential Equations, 51 (1984), pp. 326-358. | MR | Zbl
- ,[29] 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 | Zbl
,[30] 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 | Zbl
,[31] Interior gradient bounds for nonuniformly elliptic equations, Indiana Univ. Math. J., 25 (1976), pp. 821-855. | MR | Zbl
,[32] Pointwise estimates and quasilinear parabolic equations, Comm. Pure Appl. Math., 21 (1968), pp. 205-226. | MR | Zbl
,[33] The boundary gradient estimate for quasilinear elliptic and parabolic differential equations, Indiana Univ. Math. J., 21 (1972), pp. 657-670. | MR | Zbl
,[34] Fully nonlinear uniformly elliptic equations under natural structure conditions, Trans. Amer. Math. Soc., 278 (1983), pp. 751-769. | MR | Zbl
,