## 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

### Keywords:

nontangential maximal function inequalities
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### References:

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