[20201211 : 수학과세미나]
Boundary regularity for nonlocal operators with kernels of variable order
1. 일시 : 2020년 12월 11일 (금) 16:30-18:00
2. 장소 : 아산이학관 525호
3. 연사 : 이재훈 박사 (KIAS)
4. 제목 : Boundary regularity for nonlocal operators with kernels of variable order
5. 초록 : We study the boundary regularity of solutions of the Dirichlet problem
for the nonlocal operator with a kernel of variable orders. Since
the order of differentiability of the kernel is not represented by asingle
number, we consider the generalized Holder space. We prove that there
exists a unique viscosity solution of 𝐿𝑢=𝑓 in 𝐷, 𝑢=0 in R^n∖𝐷, where 𝐷 is a bounded 𝐶^1,1 open set, and that the solution 𝑢 satisfies 𝑢∈𝐶^𝑉 (𝐷) and 𝑢/𝑉(𝑑_𝐷 ) ∈𝐶^𝛼 (𝐷) with the uniform estimates, where 𝑉 is the renewal function and 𝑑_𝐷 (𝑥)=𝑑𝑖𝑠𝑡(𝑥,𝜕𝐷).
문 의 : 김일두 교수님