Solutions to the equation div u = f in weighted Sobolev spaces

Katrin Schumacher

Banach Center Publications, Tome 83 (2008), p. 433-440 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider the problem div u = f in a bounded Lipschitz domain Ω, where f with $\int_{Ω} f = 0$ is given. It is shown that the solution u, constructed as in Bogovski’s approach in [1], fulfills estimates in the weighted Sobolev spaces $W_{w}^{k, q} (Ω)$ , where the weight function w is in the class of Muckenhoupt weights $A_{q}$ .

Publié le : 2008-01-01

Zbl 1207.35095

EUDML-ID : urn:eudml:doc:282355

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     author = {Katrin Schumacher},
     title = {Solutions to the equation div u = f in weighted Sobolev spaces},
     journal = {Banach Center Publications},
     volume = {83},
     year = {2008},
     pages = {433-440},
     zbl = {1207.35095},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-26}
}

Katrin Schumacher. Solutions to the equation div u = f in weighted Sobolev spaces. Banach Center Publications, Tome 83 (2008) pp. 433-440. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-26/