Asymptotics of solutions to the Dirichlet-Cauchy problem for parabolic equations in domains with edges

Vu Trong Luong; Nguyen Manh Hung; Do Van Loi

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We give a new proof, based on analytic semigroup methods, of a maximal regularity result concerning the classical Cauchy-Dirichlet's boundary value problem for second order parabolic equations. More specifically, we find necessary and sufficient conditions on the data in order to have a strict solution $u$ which is bounded with values in $C^{2 + θ} (\bar{Ω})$ (0 < < 1), with $\partial_{t} u$ bounded with values in $C^{θ} (\bar{Ω})$ .