scholarly journals Local Regularity and Local Boundedness Results for Very Weak Solutions of Obstacle Problems

2010 ◽  
Vol 2010 (1) ◽  
pp. 878769 ◽  
Author(s):  
Gao Hongya ◽  
Qiao Jinjing ◽  
Chu Yuming
Keyword(s):  
Weak Solutions ◽  
Obstacle Problems ◽  
Local Regularity ◽  
Very Weak Solutions ◽  
Local Boundedness

scholarly journals On very weak solutions to a class of double obstacle problems

2013 ◽  
Vol 402 (2) ◽  
pp. 702-709 ◽  
Author(s):  
Gejun Bao ◽  
Tingting Wang ◽  
Guanfeng Li
Keyword(s):  
Weak Solutions ◽  
Obstacle Problems ◽  
Very Weak Solutions

REGULARITY OF VERY WEAK SOLUTIONS FOR NONHOMOGENEOUS ELLIPTIC EQUATION

2013 ◽  
Vol 15 (04) ◽  
pp. 1350012 ◽  
Author(s):  
WEI ZHANG ◽  
JIGUANG BAO
Keyword(s):  
Weak Solution ◽  
Elliptic Equation ◽  
Weak Solutions ◽  
Local Regularity ◽  
Difference Quotient ◽  
Very Weak Solutions ◽  
Very Weak Solution ◽  
Bootstrap Argument ◽  
The Difference ◽  
Higher Regularity

In this paper, we study the local regularity of very weak solution [Formula: see text] of the elliptic equation Dj(aij(x)Diu) = f - Digi. Using the bootstrap argument and the difference quotient method, we obtain that if [Formula: see text], [Formula: see text] and [Formula: see text] with 1 < p < ∞, then [Formula: see text]. Furthermore, we consider the higher regularity of u.

Local Boundedness for Very Weak Solutions of Leray-Lions Equation

2012 ◽  
Vol 457-458 ◽  
pp. 210-213
Author(s):  
Jian Tao Gu ◽  
Chun Xia Gao ◽  
Yu Xia Tong
Keyword(s):  
Weak Solution ◽  
Weak Solutions ◽  
Decomposition Methods ◽  
Hodge Decomposition ◽  
Very Weak Solutions ◽  
Local Boundedness ◽  
Very Weak Solution

The local boundedness of very weak solution of Leray-Lions equation is given in this paper by Hodge decomposition methods.

Local Boundedness for Very Weak Solutions of Leray-Lions Equation

2012 ◽  
Vol 457-458 ◽  
pp. 210-213
Author(s):  
Jian Tao Gu ◽  
Chun Xia Gao ◽  
Yu Xia Tong
Keyword(s):  
Weak Solutions ◽  
Very Weak Solutions ◽  
Local Boundedness

Regularity of the Very Weak Solutions for Double Obstacle Problems

2010 ◽  
Vol 143-144 ◽  
pp. 1396-1400
Author(s):  
Xu Juan Xu ◽  
Xiao Na Lu ◽  
Yu Xia Tong
Keyword(s):  
Elliptic Equation ◽  
Weak Solutions ◽  
Minkowski Inequality ◽  
Young Inequality ◽  
Obstacle Problems ◽  
Very Weak Solutions ◽  
Local Integrability ◽  
Regularity Results ◽  
Harmonic Equation ◽  
Homogeneous Elliptic Equation

The apply of harmonic eauation is know to all. Our interesting is to get the regularity os their solution, recently for obstacle problems. Many interesting results have been obtained for the solutions of harmonic equation ande their obstacle problems, however the double obstacle problems about the definition and regularity results for non-homogeneous elliptic equation. In this paper , the basic tool for the Young inequality,Hölder inequality, Minkowski inequality, Poincaré inequality and a basic inequality. The definition of very weak solutions for double obstacle problems associated with non-homogeneous elliptic equation is given, and the local integrability result is obtained by using the technique of Hodge decomposition.

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