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arXiv · 1205.3287

The Stokes and Poisson problem in variable exponent spaces

Lars Diening·Daniel Lengeler·Michael Ruzicka
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Abstract

We study the Stokes and Poisson problem in the context of variable exponent spaces. We prove the existence of strong and weak solutions for bounded domains with C^{1,1} boundary with inhomogenous boundary values. The result is based on generalizations of the classical theories of Calderon-Zygmund and Agmon-Douglis-Nirenberg to variable exponent spaces.

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Lars Diening, Daniel Lengeler, Michael Ruzicka. 2012-05-15. The Stokes and Poisson problem in variable exponent spaces. https://doi.org/10.1080/17476933.2010.504843

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