Ukrainian Mathematical Bulletin

Volume 2, Issue 3, 2005 pp. 323-349.

On the Solvability of the Hele-Shaw Problem in the Case of Nonsmooth Initial Data in Weighted H\"{o}lder Classes

Authors: Nataliya V. Vasylyeva
Author institution: Institute of Applied Mathematics and Mechanics of NAS of Ukraine 74 Rosa Luxemburg Str.83114, Donetsk Ukraine

Summary: We consider a nonstationary problem with a free boundary for an elliptic equation (the Hele-Shaw problem) with irregular initial data. The existence and uniqueness of a solution locally in time is proved in weighted H\"{o}lder classes.

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