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• W2002805900 abstract "In the present article we are concerned with a class of degenerate second order differential operators L A , b defined on the cube [ 0 , 1 ] d , with d ⩾ 1 . Under suitable assumptions on the coefficients A and b (among them the assumption of their Hölder regularity) we show that the operator L A , b defined on C 2 ( [ 0 , 1 ] d ) is closable and its closure is m -dissipative. In particular, its closure L A , b ¯ is the generator of a C 0 -semigroup of contractions on C ( [ 0 , 1 ] d ) and C 2 ( [ 0 , 1 ] d ) is a core for it. The proof of such result is obtained by studying the solvability in Hölder spaces of functions of the elliptic problem λ u ( x ) − L A , b u ( x ) = f ( x ) , x ∈ [ 0 , 1 ] d , for a sufficiently large class of functions f ." @default.
• W2002805900 created "2016-06-24" @default.
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• W2002805900 date "2007-11-01" @default.
• W2002805900 modified "2023-09-29" @default.
• W2002805900 title "Schauder estimates for a degenerate second order elliptic operator on a cube" @default.
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• W2002805900 doi "https://doi.org/10.1016/j.jde.2007.08.002" @default.
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