Zhongwei Shen

most citedOn Estimates of Biharmonic Functions on Lipschitz and Convex Domains

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math.AP2005★ 1 cited

On Estimates of Biharmonic Functions on Lipschitz and Convex Domains

Zhongwei Shen

Using Maz'ya type integral identities with power weights, we obtain new boundary estimates for biharmonic functions on Lipschitz and convex domains in $R^{n}$ . For $n \geq 8$ , combined…

math.AP2005

Necessary and Sufficient Conditions for the Solvability of the $L^{p}$ Dirichlet Problem On Lipschitz Domains

Zhongwei Shen

We study the homogeneous elliptic systems of order $2 ℓ$ with real constant coefficients on Lipschitz domains in $R^{n}$ , $n \geq 4$ . For any fixed $p > 2$ , we show that a reverse Höld…

math.AP2004★ 2 cited

The $L^{p}$ Dirichlet Problem for Elliptic Systems on Lipschitz Domains

Zhongwei Shen

We develop a new approach to the $L^{p}$ Dirichlet problem via $L^{2}$ estimates and reverse Holder inequalities. We apply this approach to second order elliptic systems and the polyha…

math.AP2004

Bounds of Riesz Transforms on $L^{p}$ Spaces for Second Order Elliptic Operators

Zhongwei Shen

For any fixed $p > 2$ , a necessary and sufficient condition is obtained for the boundedness of the Riesz transforms associated with second order elliptic operators with real, symmetr…

On Estimates of Biharmonic Functions on Lipschitz and Convex Domains

Necessary and Sufficient Conditions for the Solvability of the Lp Dirichlet Problem On Lipschitz Domains

The Lp Dirichlet Problem for Elliptic Systems on Lipschitz Domains

Bounds of Riesz Transforms on Lp Spaces for Second Order Elliptic Operators

Necessary and Sufficient Conditions for the Solvability of the $L^{p}$ Dirichlet Problem On Lipschitz Domains

The $L^{p}$ Dirichlet Problem for Elliptic Systems on Lipschitz Domains

Bounds of Riesz Transforms on $L^{p}$ Spaces for Second Order Elliptic Operators