Best constants and minimizers for embeddings of second order Sobolev spaces

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• 作者：Elvise Berchio and Filippo Gazzola
• 关键词：Sobolev embeddings ; Biharmonic operator ; Complementing condition
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2006
• 出版时间：15 August 2006
• 年：2006
• 卷：320
• 期：2
• 页码：718-735
• 全文大小：175 K

文摘

By considering the kernels of the first two traces, four different second order Sobolev spaces may be constructed. For these spaces, embeddings into Lebesgue spaces, the best embedding constant and the possible existence of minimizers are studied. The Euler equation corresponding to some of these minimization problems is a semilinear biharmonic equation with boundary conditions involving third order derivatives: it is shown that the complementing condition is satisfied.