Differential and Integral Equations

Some results for second order elliptic operators having unbounded coefficients

Sandra Cerrai

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By proving some estimates for the derivatives of the transition semigroup relative to a suitable stochastic equation, we prove Schauder estimates for a class of second order linear differential operators with unbounded coefficients, both in the drift and in the diffusion term. We also study asymptotic behaviour of the transition semigroup and under suitable dissipative conditions we prove existence and uniqueness of invariant measures and exponentially mixing property, uniform with respect to initial datum.

Article information

Differential Integral Equations, Volume 11, Number 4 (1998), 561-588.

First available in Project Euclid: 30 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J15: Second-order elliptic equations
Secondary: 35B40: Asymptotic behavior of solutions 35K10: Second-order parabolic equations 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 60H10: Stochastic ordinary differential equations [See also 34F05]


Cerrai, Sandra. Some results for second order elliptic operators having unbounded coefficients. Differential Integral Equations 11 (1998), no. 4, 561--588. https://projecteuclid.org/euclid.die/1367341034

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