Abstract
We use the theory of Calderón–Zygmund operators to prove regularity results for the Poisson problem and the Stokes problem, to show the solvability of the divergence equation, and to prove Korn’s inequality. These problems belong to the most classical problems treated in the theory of partial differential equations and fluid dynamics. It turns out that the treatment, especially of the whole space problems requires the notion of homogeneous Sobolev spaces, which have been studied in Sect. 12.2. The Poisson problem and the Stokes system are studied in the first two sections. After that we study the divergence equation and its consequences.
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© 2011 Springer-Verlag Berlin Heidelberg
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Diening, L., Harjulehto, P., Hästö, P., Růžička, M. (2011). PDEs and Fluid Dynamics. In: Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics(), vol 2017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18363-8_14
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DOI: https://doi.org/10.1007/978-3-642-18363-8_14
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18362-1
Online ISBN: 978-3-642-18363-8
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