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

• Autorzy: Caroline Sweezy
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 35J25: Boundary value problems for second-order elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2007
• Tom: 90
• Numer: 2
• Strony: 105-130

Daty

wydano

2007

Twórcy

autor

Caroline Sweezy

• Department of Mathematical Sciences, New Mexico State University, Box 30001 3MB, Las Cruces, NM 88003-8001, U.S.A.

Identyfikatory

DOI

10.4064/ap90-2-2