The Stokes and Poisson problem in variable exponent spaces
  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. 
Lars Diening, Daniel Lengeler, Michael Ruzicka
math.AP