中文

关于非标准增长非局部方程的Hopf引理与强最小值原理的注记

偏微分方程分析 2023-03-07 v3

摘要

ΩRn\Omega\subset \mathbb{R}^n 为任意开集,uuLu=c(x)g(u)uu\mathcal{L}u=c(x)g(|u|)\frac{u}{|u|}的弱上解,其中Lu(x)=p.v.Rng(u(x)u(y)xys)u(x)u(y)u(x)u(y)K(x,y)dyxys\mathcal{L}u(x)=\text{p.v.} \int_{\mathbb{R}^n} g\left(\frac{|u(x)-u(y)|}{|x-y|^s}\right) \frac{u(x)-u(y)}{|u(x)-u(y)|} K(x,y)\frac{dy}{|x-y|^s}g=Gg=G^{\prime}对某个Young函数GG成立。本注记给出了当c(x)c(x)Ωˉ\bar{\Omega}上连续时,uu的一类Hopf型引理与强最小值原理,推广了Del Pezzo与Quaas(JDE-2017)在分数阶Orlicz-Sobolev框架下的结果。

关键词

引用

@article{arxiv.2208.13498,
  title  = {A note on Hopf's lemma and strong minimum principle for nonlocal equations with non-standard growth},
  author = {Abhrojyoti Sen},
  journal= {arXiv preprint arXiv:2208.13498},
  year   = {2023}
}

备注

13 pages, To appear in Forum Mathematicum