当前位置: X-MOL 学术Rend. Lincei Mat. Appl. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Harnack inequality for parabolic quasi minimizers on metric spaces
Rendiconti Lincei-Matematica e Applicazioni ( IF 0.5 ) Pub Date : 2020-11-03 , DOI: 10.4171/rlm/905
Andreas Herán 1
Affiliation  

We are concerned with local parabolic quasi-minimizers $u$ on metric measure spaces. The measure space is assumed to fulfill a doubling and an annular-decay property and to support a weak (1, $p$)-Poincaré inequality, while $u$ is associated to a Carathéodory integrand $f$ obeying $p$-growth assumptions for $p \geq 2$. We are able to show a parabolic Harnack inequality under these assumptions. The quadratic case $p = 2$ has already been considered in [25], whereas the superquadratic case, at least to our knowledge, has not even been treated in the euclidean setting. The proof following the ideas of DiBenedetto, Gianazza and Vespri in [9].

中文翻译:

度量空间上抛物型拟最小化器的Harnack不等式

我们关注度量度量空间上的局部抛物线拟最小化元u。假定度量空间具有加倍和环形衰减的性质,并支持弱(1,$ p $)-庞加莱不等式,而$ u $与Carathéodory积分$ f $服从$ p $-增长相关$ p \ geq 2 $的假设。在这些假设下,我们能够证明抛物型Harnack不等式。在[25]中已经考虑了二次情况$ p = 2 $,而至少在我们所知的情况下,甚至没有在欧几里得背景中处理过二次情况。证明遵循[9]中的DiBenedetto,Gianazza和Vespri的思想。
更新日期:2020-11-04
down
wechat
bug