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math.AP2023
Sobolev space theory for Poisson's and the heat equations in non-smooth domains via superharmonic functions and Hardy's inequality
Jinsol Seo
We prove the unique solvability for the Poisson and heat equations in non-smooth domains in weighted Sobolev spaces. The zero Dirichlet boundary condition i…
math.AP2021
A weighted Sobolev regularity theory of the parabolic equations with measurable coefficients on conic domains in
Kyeonghun Kim, Kijung Lee, Jinsol Seo
We establish existence, uniqueness, and arbitrary order Sobolev regularity results for the second order parabolic equations with measurable coefficients defined on the conic domain…
math.AP2020
A refined Green's function estimate of the time measurable parabolic operators with conic domains
Kyeong-Hun Kim, Kijung Lee, Jinsol Seo
We present a refined Green's function estimate of the time measurable parabolic operators on conic domains that involves mixed weights consisting of appropriate powers of the dista…