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| HOLDER ESTIMATES FOR SOLUTIONS OF UNIFORMLY DEGENERATE QUASILINEAR PARABOLIC EQUATIONS |
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Citation： |
Chen Yazhe.HOLDER ESTIMATES FOR SOLUTIONS OF UNIFORMLY DEGENERATE QUASILINEAR PARABOLIC EQUATIONS[J].Chinese Annals of Mathematics B,1984,5(4):661~678 |
| Page view： 741
Net amount： 736 |
Authors： |
Chen Yazhe; |
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| Abstract： |
In this paper the author discusses the quasilinear parabolic equation
$$\[\frac{{\partial u}}{{\partial t}} = \frac{\partial }{{\partial {x_i}}}[{a_{ij}}(x,t,u)\frac{{\partial u}}{{\partial {x_j}}}] + {b_i}(x,t,u)\frac{{\partial u}}{{\partial {x_i}}} + c(x,t,u)\]$$
Which is uniformly degenerate at $\[u = 0\]$. Let $\[u(x,t)\]$ be a classical solution of the equation satisfying $\[0 < u(x,t) \le M\]$. Under some assumptions the author establishes the interior estimations of Holder
coefficient of the solution for the equation and the global estimations for Cauchy problems and the first boundary value problems, where Holder ooeffioients and exponents are independent of the lower positive bound of $\[u(x,t)\]$. |
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