scholarly journals Local and Global Higher Integrability of Weak Solutions to a Class of Obstacle Systems

2013 ◽  
Vol 03 (03) ◽  
pp. 215-222
Author(s):  
树清 周
Keyword(s):  
Weak Solutions ◽  
Higher Integrability ◽  
Global Higher Integrability

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 Global higher integrability of weak solutions of porous medium systems

2020 ◽  
Vol 19 (3) ◽  
pp. 1697-1745 ◽  
Author(s):  
Kristian Moring ◽  
◽  
Christoph Scheven ◽  
Sebastian Schwarzacher ◽  
Thomas Singer ◽  
...  
Keyword(s):  
Porous Medium ◽  
Weak Solutions ◽  
Higher Integrability ◽  
Global Higher Integrability

scholarly journals Higher integrability for weak solutions to a degenerate parabolic system with singular coefficients

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yan Dong ◽  
Guangwei Du ◽  
Kelei Zhang
Keyword(s):  
Parabolic System ◽  
Weak Solutions ◽  
Vector Fields ◽  
Degenerate Parabolic System ◽  
Higher Integrability ◽  
Singular Coefficients ◽  
Degenerate Parabolic ◽  
Alpha Beta ◽  
Hörmander’S Condition ◽  
Reverse Hölder

Abstract In this paper, we study the degenerate parabolic system $$ u_{t}^{i} + X_{\alpha }^{*} \bigl(a_{ij}^{\alpha \beta }(z){X_{\beta }} {u^{j}}\bigr) = {g_{i}}(z,u,Xu) + X_{\alpha }^{*} f_{i}^{\alpha }(z,u,Xu), $$ u t i + X α ∗ ( a i j α β ( z ) X β u j ) = g i ( z , u , X u ) + X α ∗ f i α ( z , u , X u ) , where $X=\{X_{1},\ldots,X_{m} \}$ X = { X 1 , … , X m } is a system of smooth real vector fields satisfying Hörmander’s condition and the coefficients $a_{ij}^{\alpha \beta }$ a i j α β are measurable functions and their skew-symmetric part can be unbounded. After proving the $L^{2}$ L 2 estimates for the weak solutions, the higher integrability is proved by establishing a reverse Hölder inequality for weak solutions.

Sign in / Sign up

Export Citation Format

Share Document