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Area integral estimates for the biharmonic operator in Lipschitz domains. (English) Zbl 0774.35022

Summary: Let \(D\subseteq\mathbb{R}^ n\) 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 \(\partial D\).

MSC:

35J40 Boundary value problems for higher-order elliptic equations
42B25 Maximal functions, Littlewood-Paley theory
35B45 A priori estimates in context of PDEs
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