Abstract
In a general unbounded uniform C 2-domain \({\Omega \subset \mathbb{R}^n, n \geq 3}\) , and \({1\leq q\leq \infty}\) consider the spaces \({\tilde{L}^q(\Omega)}\) defined by \({\tilde{L^q}(\Omega) := \left\{\begin{array}{ll}L^q(\Omega)+L^2(\Omega),\quad q < 2, \\ L^q(\Omega)\cap L^2(\Omega),\quad q\geq 2, \end{array}\right.}\) and corresponding subspaces of solenoidal vector fields, \({\tilde{L}^q_\sigma(\Omega)}\) . By studying the complex and real interpolation spaces of these we derive embedding properties for fractional order spaces related to the Stokes problem and L p − L q-type estimates for the corresponding semigroup.
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P. F. Riechwald was supported by the Studienstiftung des deutschen Volkes.
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Riechwald, P.F. Interpolation of sum and intersection spaces of L q-type and applications to the Stokes problem in general unbounded domains. Ann Univ Ferrara 58, 167–181 (2012). https://doi.org/10.1007/s11565-011-0140-6
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DOI: https://doi.org/10.1007/s11565-011-0140-6