caa a22 4500 445836458 CHVBK 20180317145331.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00209-009-0622-8 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0622-8 Huber Alexander Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103, Leipzig, Germany aut The divergence equation in weighted- and L p (·)-spaces [Elektronische Daten] [Alexander Huber] We study the solvability of the divergence equation in weighted spaces and Lebesgue spaces with variable exponents, where the weights are so called Muckenhoupt weights. The question of constructing divergence free test functions, which can be used for problems arising in fluid dynamics, is also addressed. The approach is based on an explicit representation formula for solutions of the divergence equation due to Bogovskiĭ and the theory of singular integral operators. The developed methods are used to prove an existence result for fluids which satisfy a p(·)-growth condition. The Author(s), 2009 Divergence equation nationallicence Muckenhoupt weights nationallicence Lebesgue spaces with variable exponents nationallicence Singular integrals nationallicence Fluids with p (·)-growth nationallicence Mathematische Zeitschrift Springer-Verlag 267/1-2(2011-02-01), 341-366 0025-5874 267:1-2<341 2011 267 209 https://doi.org/10.1007/s00209-009-0622-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0622-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Huber Alexander Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103, Leipzig, Germany aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/1-2(2011-02-01), 341-366 0025-5874 267:1-2<341 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer