9 citations · 11 across the 5 of their papers we have counts for
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Trace theorem and non-zero boundary value problem for parabolic equations in weighted Sobolev spaces
Doyoon Kim, Kyeong-Hun Kim, Kwan Woo
We present weighted Sobolev spaces and prove a trace theorem for the spaces. As an application, we discuss non-zero boundary value problems for parabolic equations. The weighted pa…
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…
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…
An -theory for the time fractional evolution equations with variable coefficients
Ildoo Kim, Kyeong-Hun Kim, Sungbin Lim
We introduce an -theory for the quasi-linear fractional equations of the type $$ \partial^α_t u(t,x)=a^{ij}(t,x)u_{x^i x^j}(t,x)+f(t,x,u), \quad t>0, \,x\in \mathbf{R}^d.…