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

Annales Polonici Mathematici (2007)

- Volume: 90, Issue: 2, page 105-130
- ISSN: 0066-2216

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topCaroline Sweezy. "A Littlewood-Paley type inequality with applications to the elliptic Dirichlet problem." Annales Polonici Mathematici 90.2 (2007): 105-130. <http://eudml.org/doc/280936>.

@article{CarolineSweezy2007,

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

author = {Caroline Sweezy},

journal = {Annales Polonici Mathematici},

keywords = {elliptic equations; Lipschitz domains; Littlewood-Paley type inequalities},

language = {eng},

number = {2},

pages = {105-130},

title = {A Littlewood-Paley type inequality with applications to the elliptic Dirichlet problem},

url = {http://eudml.org/doc/280936},

volume = {90},

year = {2007},

}

TY - JOUR

AU - Caroline Sweezy

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

JO - Annales Polonici Mathematici

PY - 2007

VL - 90

IS - 2

SP - 105

EP - 130

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

LA - eng

KW - elliptic equations; Lipschitz domains; Littlewood-Paley type inequalities

UR - http://eudml.org/doc/280936

ER -

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