Ukrainian Mathematical Bulletin

Volume 3, Issue 4, 2006 pp. 423-446.

On Optimal Regularity of Solutions of the First Boundary Value Problem for a Class of Degenerate Elliptic Equations

Authors: Sergei P. Degtyarev
Author institution: Institute of Applied Mathematics and Mechanics of NAS of Ukraine, 74 Rosa Luxemburg Str., 83114, Donetsk, Ukraine, spdeg@yahoo.com

Summary: We study the first boundary value problem for a degenerate elliptic equation. This problem, in particular, is obtained when studying the motion of a fluid. We find natural H\"older and Sobolev spaces on which the operator of the problem becomes Fredholm. We also obtain exact coercive estimates for a solution in the above classes. It was found, in particular, that smoothness of a solution of the problem is limited, even if the data is infinitely smooth.

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