Global estimates for nonlinear parabolic equations

被引：8
|
作者：
Baroni, Paolo [1 ]
Di Castro, Agnese [2 ]
Palatucci, Giampiero [2 ]
机构：
[1] Scuola Normale Super Pisa, I-56126 Pisa, Italy
[2] Univ Parma, Dipartimento Matemat & Informat, I-43124 Parma, Italy
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2013年 / 13卷 / 01期
关键词：
Nonlinear parabolic problems; Calderon-Zygmund theory; Lorentz regularity; Rearrangement invariant function spaces; Higher integrability; RENORMALIZED SOLUTIONS; SYSTEMS; REGULARITY; INTEGRABILITY; POTENTIALS;
D O I：
10.1007/s00028-013-0174-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider nonlinear parabolic equations of the type u(t) - diva(x,t, Du) = f(x,t) on Omega(T) = Omega x (-T,0), under standard growth conditions on a, with f only assumed to be integrable. We prove general decay estimates up to the boundary for level sets of the solutions u and the gradient Du which imply very general estimates in Lebesgue and Lorentz spaces. Assuming only that the involved domains satisfy a mild exterior capacity density condition, we provide global regularity results.
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页码：163 / 195
页数：33
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