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Regularity of solutions to the polyharmonic equation in general domains
Regularity of solutions polyharmonic equation general domains Analysis of PDEs
2012/6/9
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 $\RR^n$, $2\leq n\leq 2m...
Polyharmonic Hardy Spaces on the Complexified Annulus and Error Estimates of Cubature Formulas
Hardy space Numerical Integration Cubature formulas Error estimate
2012/4/23
The present paper has a twofold contribution: first, we introduce a new concept of Hardy spaces on a multidimensional complexified annular domain which is closely related to the annulus of the Klein-D...
Isolated Singularities of Nonlinear Polyharmonic Inequalities
Isolated singularity Polyharmonic Analysis of PDEs
2011/9/19
Abstract: We obtain results for the following question where $m\ge 1$ and $n\ge 2$ are integers. {\bf Question.} For which continuous functions $f\colon [0,\infty)\to [0,\infty)$ does there exist a co...
Polyharmonic and Related Kernels on Manifolds: Interpolation and Approximation
manifold positive definite kernels least squares approximation Sobolev spaces
2011/2/24
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting.