Gradient estimates for a quasilinear parabolic equation of the mean curvature type

Mitsuhiro NAKAO; Yasuhiro OHARA

doi:10.2969/jmsj/04830455

Mitsuhiro NAKAO, Yasuhiro OHARA

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JOURNAL FREE ACCESS

1996 Volume 48 Issue 3 Pages 455-466

DOI https://doi.org/10.2969/jmsj/04830455

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Published: 1996 Received: September 07, 1994 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) N. D. Alikakos and R. Rostamian, Gradient estimates for degenerate diffusion equations, Math. Ann., 259 (1982), 53-70.
2) H. Engler, B. Kawohl and S. Luckhaus, Gradient estimates for solutions of parabolic equations and systems, J. Math. Anal. Appl., 147 (1990), 309-329.
3) O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, AMS, Providence, RI, 1968.
4) A. Lichnewsky and R. Temam, Pseudosolutions of the time-dependent minimal surface problem, J. Differential Equations, 30 (1978), 340-364.
5) M. Nakao, Global solutions for some nonlinear parabolic equations with nonmonotonic perturbations, Nonlinear Anal. T.M.A., 10 (1986), 299-314.
6) M. Nakao, Energy decay for the quasilinear wave equation with viscosity, Math. Z., to appear.
7) Y. Ohara, L^∞-estimates of solutions of some nonlinear degenerate parabolic equations, Nonlinear Anal. T.M.A., 18 (1992), 413-426.
8) V. I. Oliker and N. N. Uraltseva, Evolution of nonparametric surfaces with speed depending on curvature II. The mean curvature case, Comm. Pure Appl. Math., XLVI (1993), 97-139.
9) J. Serrin, The problem of Dirichlet for quasilinear elliptic differential equation with many independent variables, Philos. Trans. Roy. Soc. London Ser. A, 264 (1969), 413-496.
10) L. Véron, Coercivité et propriétés régularisantes des semi-groupes non linéaires dans les espaces de Banach, Faculté des Sciences et Techniques, Université Francois Rabelais-Tours, France, 1976.

Right : [1] N. D. Alikakos and R. Rostamian, Gradient estimates for degenerate diffusion equations, Math. Ann., 259 (1982), 53-70.
[2] H. Engler, B. Kawohl and S. Luckhaus, Gradient estimates for solutions of parabolic equations and systems, J. Math. Anal. Appl., 147 (1990), 309-329.
[3] O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, AMS, Providence, RI, 1968.
[4] A. Lichnewsky and R. Temam, Pseudosolutions of the time-dependent minimal surface problem, J. Differential Equations, 30 (1978), 340-364.
[5] M. Nakao, Global solutions for some nonlinear parabolic equations with nonmonotonic perturbations, Nonlinear Anal. T. M. A., 10 (1986), 299-314.
[6] M. Nakao, Energy decay for the quasilinear wave equation with viscosity, Math. Z., to appear.
[7] Y. Ohara, L^∞-estimates of solutions of some nonlinear degenerate parabolic equations, Nonlinear Anal. T.M.A., 18 (1992), 413-426.
[8] V. I. Oliker and N. N. Uraltseva, Evolution of nonparametric surfaces with speed depending on curvature II. The mean curvature case, Comm. Pure Appl. Math., XLVI (1993), 97-139.
[9] J. Serrin, The problem of Dirichlet for quasilinear elliptic differential equation with many independent variables, Philos. Trans. Roy. Soc. London Ser. A, 264 (1969), 413-496.
[10] L. Véron, Coercivité et propriétés régularisantes des semi-groupes non linéaires dans les espaces de Banach, Faculté des Sciences et Techniques, Université Francois Rabelais-Tours, France, 1976.

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