Density results with linear combinations of translates of fundamental solutions

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• 作者：Yiorgos-Sokratis Smyrlis
• 关键词：Fundamental solutions ; Elliptic partial differential equations ; Elliptic systems ; Approximation by special functions ; Method of fundamental solutions ; Universal series
• 刊名：Journal of Approximation Theory
• 出版年：2009
• 出版时间：December 2009
• 年：2009
• 卷：161
• 期：2
• 页码：617-633
• 全文大小：743 K

文摘

In the present work, we investigate the approximability of solutions of elliptic partial differential equations in a bounded domain Ω by linear combinations of translates of fundamental solutions of the underlying partial differential operator. The singularities of the fundamental solutions lie outside of . The domains under consideration may possess holes and they are required to satisfy a rather mild boundary regularity requirement, namely the segment condition. We study approximations with respect to the norms of the spaces and the spaces of uniformly Hölder continuous functions , and we establish density and non-density results for elliptic operators with constant coefficients. We also provide applications of our density results related to the method of fundamental solutions and to the theory of universal series.