The regularity of generalized solutions for the n-dimensional quasi-linear parabolic diffraction problems |
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Authors: | Qi-Jian Tan Zhong-Jian Leng |
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Affiliation: | 1. Department of Mathematics, Sichuan College of Education, Chengdu 610041, China;2. College of Mathematics, Sichuan University, Chengdu, 610064, China |
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Abstract: | In this paper, we study the regularity of generalized solutions u(x,t) for the n -dimensional quasi-linear parabolic diffraction problem. By using various estimates and Steklov average methods, we prove that (1): for almost all t the first derivatives ux(x,t) are Hölder continuous with respect to x up to the inner boundary, on which the coefficients of the equation are allowed to be discontinuous; and (2): the first derivative ut(x,t) is Hölder continuous with respect to (x,t) across the inner boundary. |
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Keywords: | 35K20 35R05 |
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