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Estimates of the derivatives for a class of parabolic degenerate operators with unbounded coefficients in \(\mathbb R^N\). (English) Zbl 1107.35071
The paper deals with a class of perturbations of the degenerate Ornstein-Uhlenbeck operator in \(\mathbb R^N.\) By virtue of a revised version of the Bernstein method, the author obtains various uniform estimates for the semigroup \(\{T(t)\}_{t\geq0}\) associated with the realization of a degenerate elliptic operator in the space of the bounded and continuous functions in \(\mathbb R^N.\)

MSC:
35K65 Degenerate parabolic equations
35B65 Smoothness and regularity of solutions to PDEs
47D06 One-parameter semigroups and linear evolution equations
35B45 A priori estimates in context of PDEs
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References:
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