Nonlocal Harnack inequalities for nonlocal heat equations
Nonlocal Harnack inequalities for nonlocal heat equations
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DOI：
10.1016/j.jde.2019.07.006
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发表时间：
2019-11-15
影响因子：
2.4
通讯作者：
Kim, Yong-Cheol
中科院分区：
文献类型：
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作者：
Kim, Yong-Cheol
通过应用 De Giorgi-Nash-Moser 理论，我们获得由积分微分算子 L-K 给出的非局部抛物型方程的局部非负弱解的非局部 Harnack 不等式，如下所示：{L(K)u + 偏导数(t)u = 0 in Omega(I) := Omega x (-T, 0]u = g in偏 导数(p)Omega(I) : = ((R-n\Omega) x (-T, 0]) 布尔 OR(Omega x {t = -T})for g 是 C(R-I*(n)) 的元素 AND L-无穷大 (R-n x (-T, 0]) 布尔 AND H-T(s)(R-n) 以及 R-n 的有界域 Omega 子集利普希茨 边界。有趣的是，这个结果暗示了全局非负弱解的经典 Harnack 不等式。 (C) 2019 Elsevier Inc. 保留所有权利。
By applying the De Giorgi-Nash-Moser theory, we obtain nonlocal Harnack inequalities for locally non-negative weak solutions of nonlocal parabolic equations given by an integro-differential operator L-K as follows:{L(K)u + partial derivative(t)u = 0 in Omega(I) := Omega x (-T, 0]u = g in partial derivative(p)Omega(I) : = ((R-n\Omega) x (-T, 0]) boolean OR(Omega x {t = -T})for g is an element of C(R-I*(n)) boolean AND L-infinity (R-n x (-T, 0]) boolean AND H-T(s)(R-n) and a bounded domain Omega subset of R-n with Lipschitz boundary. Interestingly, this result implies the classical Harnack inequalities for globally nonnegative weak solutions. (C) 2019 Elsevier Inc. All rights reserved.