论文标题
在大型汉密尔顿 - 雅各比方程的大型解决方案上
On large solutions for fractional Hamilton-Jacobi equations
论文作者
论文摘要
我们研究了在有限的，平稳的域上提出的非本地差异问题的大解决方案，该域与订单$ 2S $的完全非线性椭圆方程相关，其中$ s \ in（1/2,1）$，以及具有亚临界功率$ 0 <p <p <2s $的强制梯度术语。 由于扩散的非本地性质，新的爆炸现象在$ 0 <p <2s $范围内出现，涉及一个连续的解决方案和/或边界上损失$ - \ infty $的解决方案。这与Lasry-Lions为案例次级案例$ 1 <p <2 $研究的当地案例有惊人的差异。
We study the existence of large solutions for nonlocal Dirichlet problems posed on a bounded, smooth domain, associated to fully nonlinear elliptic equations of order $2s$, with $s\in (1/2,1)$, and a coercive gradient term with subcritical power $0<p<2s$. Due to the nonlocal nature of the diffusion, new blow-up phenomena arise within the range $0<p<2s$, involving a continuum family of solutions and/or solutions blowing-up to $-\infty$ on the boundary. This is in striking difference with the local case studied by Lasry-Lions for the case subquadratic case $1<p<2$.
