Gradient bounds for solutions of semilinear parabolic equations without Bernstein's quadratic condition |
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| Authors: | Jean-Philippe Bartier Philippe Souplet |
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| Institution: | 1. Ceremade, UMR CNRS 7534, Université Paris IX – Dauphine, place de Lattre de Tassigny, 75775 Paris cedex 16, France;2. Laboratoire de mathématiques appliquées, UMR CNRS 7641, Université de Versailles, 45, avenue des États-Unis, 78035 Versailles, France;3. Département de mathématiques, Université de Picardie, INSSET, 02109 Saint-Quentin, France |
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| Abstract: | We establish gradient estimates for bounded solutions of semilinear parabolic equations, where the nonlinearity only satisfies one-sided quadratic upper growth assumptions, instead of the classical (two-sided) Bernstein's condition. This extends a recent work of Al. and Ar. Tersenov (Indiana Univ. Math. J. 50 (2001) 1899–1913), where results of this kind were obtained for radial solutions in a ball, by a different technique. To cite this article: J.-Ph. Bartier, Ph. Souplet, C. R. Acad. Sci. Paris, Ser. I 338 (2004). |
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