$L_q(L_p)$-theory of parabolic PDE$\mathbf{s}$ with variable coefficients
Bull. Korean Math. Soc. 2008 Vol. 45, No. 1, 169-190
Printed March 1, 2008
Kyeong-Hun Kim
Korea University
Abstract : Second-order parabolic equations with variable coefficients are considered on $\mathbb R^d$ and $C^1$ domains. Existence and uniqueness results are given in $L_q(L_p)$-spaces, where it is allowed for the powers of summability with respect to space and time variables to be different.
Keywords : parabolic equations, $L_q(L_p)$-theory, Sobolev spaces with weights
MSC numbers : 35K10
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