The Stokes and Poisson problem in variable exponent spaces

Abstract

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

Keywords:

• variable exponent space
• Stokes problem
• Poisson problem

AMS Subject Classifications::

• 35Q35
• 35J05
• 35D30
• 35D35
• 32A55
• 46E30

Notes

Note

1. As we already pointed out it is considerably simpler to obtain the half-space results in the case of the Poisson problem.