A Littlewood-Paley type inequality with applications to the elliptic Dirichlet problem

Caroline Sweezy

Caroline Sweezy

Annales Polonici Mathematici, Tome 92 (2007), p. 105-130 / Harvested from The Polish Digital Mathematics Library

Résumé

Let L be a strictly elliptic second order operator on a bounded domain Ω ⊂ ℝⁿ. Let u be a solution to $L u = d i v \vec{f}$ in Ω, u = 0 on ∂Ω. Sufficient conditions on two measures, μ and ν defined on Ω, are established which imply that the $L^{q} (Ω, d μ)$ norm of |∇u| is dominated by the $L^{p} (Ω, d v)$ norms of $d i v \vec{f}$ and $| \vec{f} |$ . If we replace |∇u| by a local Hölder norm of u, the conditions on μ and ν can be significantly weaker.

Publié le : 2007-01-01

Zbl 1134.35040

EUDML-ID : urn:eudml:doc:280936

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     title = {A Littlewood-Paley type inequality with applications to the elliptic Dirichlet problem},
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     volume = {92},
     year = {2007},
     pages = {105-130},
     zbl = {1134.35040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-2-2}
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Caroline Sweezy. A Littlewood-Paley type inequality with applications to the elliptic Dirichlet problem. Annales Polonici Mathematici, Tome 92 (2007) pp. 105-130. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-2-2/