Global higher integrability for the parabolic equations in Reifenberg domains

2010 ◽  
Vol 283 (9) ◽  
pp. 1358-1367 ◽  
Author(s):  
Fengping Yao
Keyword(s):  
Parabolic Equations ◽  
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 Global higher integrability for minimisers of convex functionals with (p,q)-growth

2021 ◽  
Vol 60 (2) ◽  
Author(s):  
Lukas Koch
Keyword(s):  
Hölder Continuity ◽  
Growth Conditions ◽  
Holder Continuity ◽  
Higher Integrability ◽  
Convex Functionals ◽  
Global Higher Integrability ◽  
Continuity Assumption

AbstractWe prove global $$W^{1,q}({\varOmega },{\mathbb {R}}^m)$$ W 1 , q ( Ω , R m ) -regularity for minimisers of convex functionals of the form $${\mathscr {F}}(u)=\int _{\varOmega } F(x,Du)\,{\mathrm{d}}x$$ F ( u ) = ∫ Ω F ( x , D u ) d x .$$W^{1,q}({\varOmega },{\mathbb {R}}^m)$$ W 1 , q ( Ω , R m ) regularity is also proven for minimisers of the associated relaxed functional. Our main assumptions on F(x, z) are a uniform $$\alpha $$ α -Hölder continuity assumption in x and controlled (p, q)-growth conditions in z with $$q<\frac{(n+\alpha )p}{n}$$ q < ( n + α ) p n .

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