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On Sobolev solutions of poisson equations in ℝd with a parameter

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Smoothness with respect to a parameter is established under mild assumptions on the regularity of coefficients for Sobolev solutions of the Poisson equations in the whole ℝd in the “ergodic case.” An assertion of this kind serves as one of the key tools in diffusion approximation and some other limit theorems. Bibliography: 12 titles.

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  1. School of Mathematics, University of Leeds, LS2 9JT, UK Institute of Information Transmission Problems, RAS, Moscow, Russia

    A. Yu. Veretennikov

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  1. A. Yu. Veretennikov
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Correspondence to A. Yu. Veretennikov.

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To the 70th birthday of Professor N. V. Krylov

Translated from Problems in Mathematical Analysis 61, October 2011, pp. 43–68.

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Veretennikov, A.Y. On Sobolev solutions of poisson equations in ℝd with a parameter. J Math Sci 179, 48–79 (2011). https://doi.org/10.1007/s10958-011-0582-5

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  • DOI: https://doi.org/10.1007/s10958-011-0582-5

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