Abstract
Let (M,g) be a complete noncompact Riemannian manifold. In this note, we derive a local Hamilton-type gradient estimate for positive solution to a simple nonlinear parabolic equation
on M × (0,∞), where a is a constant and q is a C 2 function. This result can be compared with the ones of Ma (JFA, 241, 374–382 (2006)) and Yang (PAMS, 136, 4095–4102 (2008)). Also, we obtain Hamilton’s gradient estimate for the Schödinger equation. This can be compared with the result of Ruan (JGP, 58, 962–966 (2008)).
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Supported by the China Scholarship Council of China (Grant No. 2007U13020) during the 2007–2009 Academic Year
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Qian, B. Hamilton-type gradient estimates for a nonlinear parabolic equation on Riemannian manifolds. Acta. Math. Sin.-English Ser. 27, 1071–1078 (2011). https://doi.org/10.1007/s10114-011-8474-7
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DOI: https://doi.org/10.1007/s10114-011-8474-7