Regularity results for the solutions of the Dirichlet problems on snowflake domains.

What is it about?

The aim of the paper is to establish estimates in weighted Sobolev spaces for the solutions of the Dirichlet problems on snowflake domains. Moreover we obtain uniform estimates(in weighted Sobolev spaces) for the solutions of the Dirichlet problems on pre-fractal approximating domains.

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Why is it important?

Best estimates of regularity for the first and the second derivatives of the solution to the Dirichlet problem on snowflake domain.