﻿ 双调和抛物方程的加权Lp估计 Weighted Lp Estimates for the Bi-Harmonic Parabolic Equation

Pure Mathematics
Vol.05 No.02(2015), Article ID:14904,7 pages
10.12677/PM.2015.52007

Weighted Lp Estimates for the Bi-Harmonic Parabolic Equation

Huacui Yu

College of Sciencers, Shanghai University, Shanghai

Email: 15202161183@163.com

Received: Feb. 18th, 2015; accepted: Feb. 27th, 2015; published: Mar. 3rd, 2015

ABSTRACT

Schauder estimates and estimates are the basic regularity estimates in the partial differential equations. In this paper we mainly study a new class of regularity estimates, weighted estimates for the bi-harmonic parabolic equation.

Keywords:Bi-Harmonic Parabolic Equation, Weighted, Estimates, Regularity Estimates

Email: 15202161183@163.com

Schauder估计和估计是偏微分方程基本的正则性估计。本文我们主要研究双调和抛物方程的一类新的正则性估计——加权估计。

1. 引言

(1.1)

(1.2)

2) 如果，那么，

3) 如果，那么，

4) 如果，那么

(1.3)

(1.4)

2. 主要结论的证明

(2.1)

(2.2)

(2.3)

(2.4)

(2.5)

(2.6)

2) 由(2.2)和(2.3)，可得：

(2.7)

(2.8)

.

(2.9)

，可知

(2.10)

Weighted Lp Estimates for the Bi-Harmonic Parabolic Equation. 理论数学,02,46-53. doi: 10.12677/PM.2015.52007

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