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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.PR2021
Sobolev space theory and Hölder estimates for the stochastic partial differential equations on conic and polygonal domains
Kyeong-Hun Kim, Kijung lee, Jinsol Seo
We establish existence, uniqueness, and Sobolev and Hölder regularity results for the stochastic partial differential equation $$ du=\left(\sum_{i,j=1}^d a^{ij}u_{x^ix^j}+f^0+\sum_…