Solutions to the equation ${\rm div} u=f$ in weighted Sobolev spaces

Tom 81 / 2008

Katrin Schumacher Banach Center Publications 81 (2008), 433-440 MSC: Primary 35F15. DOI: 10.4064/bc81-0-26

Streszczenie

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 $A_q$.

Autorzy

  • Katrin SchumacherDepartment of Mathematics
    Technische Universität Darmstadt
    Schlossgartenstraße 7
    64289 Darmstadt, Germany
    e-mail

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