Solutions to the equation ${\rm div} u=f$ in weighted Sobolev spaces
Volume 81 / 2008
Banach Center Publications 81 (2008), 433-440
MSC: Primary 35F15.
DOI: 10.4064/bc81-0-26
Abstract
We consider the problem $\mathop{\rm div} u=f$ in a bounded Lipschitz domain $\Omega$, where $f$ with $\int_\Omega f=0$ is given. It is shown that the solution $u$, constructed as in Bogovski's approach in [1], fulfills estimates in the weighted Sobolev spaces $W^{k,q}_{w}(\Omega)$, where the weight function $w$ is in the class of Muckenhoupt weights $A_q$.
