scholarly journals Local boundedness results for very weak solutions of double obstacle problems

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Yuxia Tong ◽  
Juan Li ◽  
Jiantao Gu
Keyword(s):  
Weak Solutions ◽  
Obstacle Problems ◽  
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

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.

scholarly journals Higher Integrability of Weak Solutions to a Class of Double Obstacle Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhenhua Hu ◽  
Shuqing Zhou
Keyword(s):  
Differential Equation ◽  
Weak Solutions ◽  
Second Order ◽  
Obstacle Problems ◽  
Elliptic Differential Equation ◽  
Higher Integrability ◽  
Global Higher Integrability ◽  
Quasilinear Elliptic

We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equationdiv(A(x,∇u))=div f(x,u), whereA(x,∇u),f(x,u)are twon×Nmatrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems.

scholarly journals Uniqueness of very weak solutions for a fractional filtration equation

2020 ◽  
Vol 365 ◽  
pp. 107041 ◽  
Author(s):  
Gabriele Grillo ◽  
Matteo Muratori ◽  
Fabio Punzo
Keyword(s):  
Weak Solutions ◽  
Very Weak Solutions ◽  
Filtration Equation
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