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Area integral estimates for the biharmonic operator in Lipschitz domains


Authors: Jill Pipher and Gregory Verchota
Journal: Trans. Amer. Math. Soc. 327 (1991), 903-917
MSC: Primary 35J40; Secondary 35B65
DOI: https://doi.org/10.1090/S0002-9947-1991-1024776-7
MathSciNet review: 1024776
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Abstract: Let $ D \subseteq {{\mathbf{R}}^n}$ be a Lipschitz domain and let $ u$ be a function biharmonic in $ D$, i.e., $ \Delta \Delta u= 0$ in $ D$. We prove that the nontangential maximal function and the square function of the gradient of $ u$ have equivalent $ {L^p}(d\mu)$ norms, where $ d\mu \in {A^\infty }\,(d\sigma)$ and $ d\sigma $ is surface measure on $ \partial D$.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1024776-7
Article copyright: © Copyright 1991 American Mathematical Society

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