Global higher integrability for minimisers of convex functionals with (p,q)-growth
2021 ◽
Vol 60
(2)
◽
Keyword(s):
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 .
1990 ◽
Vol 150
(1)
◽
pp. 161-165
◽
2011 ◽
Vol 284
(11-12)
◽
pp. 1404-1434
◽
Keyword(s):
2005 ◽
Vol 22
(3)
◽
pp. 793-806
◽
2015 ◽
Vol 195
(5)
◽
pp. 1405-1461
◽
Keyword(s):