2012/06/01 by Svitlana Mayboroda, Mayboroda, Svitlana, Vladimir Maz’ya +1
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1206.0081
The present paper establishes boundedness of [m-\frac n2+\frac 12] derivatives for the solutions to the polyharmonic equation of order 2m in arbitrary bounded open sets of \RRn, 2≤ n≤ 2m+1, without any restrictions on the geometry of the underlying domain. It is shown that this result is sharp and cannot be improved in general domains. Moreover, it is accompanied by sharp estimates on the polyharmonic Green function.