非局部双相抛物方程变分解的局部有界性
偏微分方程分析
2022-02-21 v2
摘要
我们证明了双相方程变分解的局部有界性 \begin{align*} \partial_t u +& P.V.\int_{\mathbb{R}^N}\frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+ps}}\\ &+a(x,y)\frac{|u(x,t)-u(y,t)|^{q-2}(u(x,t)-u(y,t))}{|x-y|^{N+qs'}} \,dy = 0, \end{align*} 在限制条件 下,且非负函数 假设为可测且有界。
引用
@article{arxiv.2112.02345,
title = {Local boundedness of variational solutions to nonlocal double phase parabolic equations},
author = {Harsh Prasad and Vivek Tewary},
journal= {arXiv preprint arXiv:2112.02345},
year = {2022}
}
备注
30 pages, subcritical case was added, time-dependence of H was removed