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

著者情報

ジャーナルフリー

1996 年 48 巻 3 号 p. 455-466

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

詳細

Published: 1996 Received: 1994/09/07 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: 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.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

責任著者(Corresponding author)

訂正情報

J-STAGEへの登録はこちら（無料）