Geometric character of domain and the Harnack inequality of solution of a singular parabolic equation |
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Authors: | Jiaqing Pan |
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Institution: | 1. Mathematical Institute, Jimei University, Xiamen, 361021, P. R. China
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Abstract: | The geometric character of domains of solutions of a singular parabolic equation with the Neumann boundary condition are discussed in this work. We prove a gradient estimate and a Harnack type inequality and then, show that the domains of the solutions are exactly columns in the space-time. Specially, the altitudes of the columns are calculated accurately. |
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