Area integral estimates for the biharmonic operator in lipschitz domains

Jill Pipher; Gregory Verchota

doi:10.1090/S0002-9947-1991-1024776-7

Area integral estimates for the biharmonic operator in lipschitz domains

Jill Pipher, Gregory Verchota

Department of Mathematics

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18 Scopus citations

Abstract

Let D ⊆ Rⁿ be a Lipschitz domain and let u be a function biharmonic in D, i.e., ΔΔu = 0 in D. We prove that the nontangential maximal function and the square function of the gradient of u have equivalent L^p(dµ) norms, where d µ ϵ A^∞(do) and dσ is surface measure on ∂D.

Original language	English (US)
Pages (from-to)	903-917
Number of pages	15
Journal	Transactions of the American Mathematical Society
Volume	327
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1991-1024776-7
State	Published - Oct 1991

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-1991-1024776-7

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title = "Area integral estimates for the biharmonic operator in lipschitz domains",

abstract = "Let D ⊆ Rn be a Lipschitz domain and let u be a function biharmonic in D, i.e., ΔΔu = 0 in D. We prove that the nontangential maximal function and the square function of the gradient of u have equivalent Lp(dµ) norms, where d µ ϵ A∞(do) and dσ is surface measure on ∂D.",

author = "Jill Pipher and Gregory Verchota",

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N2 - Let D ⊆ Rn be a Lipschitz domain and let u be a function biharmonic in D, i.e., ΔΔu = 0 in D. We prove that the nontangential maximal function and the square function of the gradient of u have equivalent Lp(dµ) norms, where d µ ϵ A∞(do) and dσ is surface measure on ∂D.

AB - Let D ⊆ Rn be a Lipschitz domain and let u be a function biharmonic in D, i.e., ΔΔu = 0 in D. We prove that the nontangential maximal function and the square function of the gradient of u have equivalent Lp(dµ) norms, where d µ ϵ A∞(do) and dσ is surface measure on ∂D.

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ER -

Area integral estimates for the biharmonic operator in lipschitz domains

Abstract

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