A gradient estimate for solutions to parabolic equations with discontinuous coefficients
A gradient estimate for solutions to parabolic equations with discontinuous coefficients
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具有不连续系数的抛物线方程解的梯度估计
DOI：
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发表时间：
2011-03
影响因子：
0.7
通讯作者：
Nakamura, Gen
中科院分区：
文献类型：
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作者：
Fan, Jishan;Kim, Kyoungsun;Nagayasu, Sei;Nakamura, Gen
Li-Vogelius和Li-Nirenberg分别给出了强椭圆型方程和具有分段光滑系数的散度型方程组解的梯度估计。假设系数的不连续性由余维为1的流形给出，我们称之为不连续流形。它们的梯度估计与不连续流形之间的距离无关。在本文中，我们给出了他们的结果的一个抛物线形式。也就是说，我们给出了具有分段光滑系数的散度型抛物方程的梯度估计。系数被假定为与时间无关，并且它们的不连续性与前面的椭圆方程相同。作为这个估计的应用，我们还给出了一个具有分段光滑系数的抛物型算子基本解的逐点梯度估计。这两种梯度估计与不连续流形之间的距离无关。
Li-Vogelius and Li-Nirenberg gave a gradient estimate for solutions of strongly elliptic equations and systems of divergence forms with piecewise smooth coefficients, respectively. The discontinuities of the coefficients are assumed to be given by manifolds of codimension 1, which we called them manifolds of discontinuities. Their gradient estimate is independent of the distances between manifolds of discontinuities. In this paper, we gave a parabolic version of their results. That is, we gave a gradient estimate for parabolic equations of divergence forms with piecewise smooth coefficients. The coefficients are assumed to be independent of time and their discontinuities are likewise the previous elliptic equations. As an application of this estimate, we also gave a pointwise gradient estimate for the fundamental solution of a parabolic operator with piecewise smooth coefficients. The both gradient estimates are independent of the distances between manifolds of discontinuities.
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影响因子：
1.3
作者：
Kazuki Yoshida
通讯作者：
Kazuki Yoshida
影响因子：
2.5
作者：
Yanyan Li;M. Vogelius
通讯作者：
Yanyan Li;M. Vogelius
DOI：
10.1137/090759719
发表时间：
2009-04
期刊：
SIAM J. Math. Anal.
影响因子：
--
作者：
M. Cristo;S. Vessella
通讯作者：
M. Cristo;S. Vessella
DOI：
10.1142/9789812702548_0014
发表时间：
2004-06
期刊：
--
影响因子：
--
作者：
L. Nirenberg
通讯作者：
L. Nirenberg
影响因子：
2.5
作者：
E. Fabes;E. Fabes;D. Stroock;D. Stroock
通讯作者：
E. Fabes;E. Fabes;D. Stroock;D. Stroock