Global higher integrability for minimisers of convex obstacle problems with (p,q)-growth

被引：10
作者：
Koch, Lukas [1 ]
机构：
[1] Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2022年 / 61卷 / 03期
基金：
英国工程与自然科学研究理事会;
关键词：
ELLIPTIC-EQUATIONS; PENALTY METHOD; REGULARITY; FUNCTIONALS; GROWTH; INTEGRALS; CALCULUS; RELAXATION; BESOV;
D O I：
10.1007/s00526-022-02202-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove global W-1,W-q(Omega,R-N)-regularity for minimisers of F(u)=integral F-Omega(x,Du) dx satisfying u >= psi for a given Sobolev obstacle psi W-1,W-q (Omega, R-N) regularity is also proven for minimisers of the associated relaxed functional. Our main assumptions on F(x, z) are a uniform alpha-Holder continuity assumption in x and natural ( p, q)-growth conditions in z with q < (n+alpha)p/n. In the autonomous case F = F(z) we can yimprove the gap to q < min (np/n-1, p + 1), a result new even in the unconstrained case.
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页数：28
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