On estimates of biharmonic functions on Lipschitz and convex domains

DOI10.1007/BF02922138zbMath1174.31306arXivmath/0510053MaRDI QIDQ2508674

Zhongwei Shen

Publication date: 20 October 2006

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0510053

zbMATH Keywords

biharmonic functionsLipschitz and convex domains

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Biharmonic and polyharmonic equations and functions in higher dimensions (31B30)

Related Items

Higher-Order Elliptic Equations in Non-Smooth Domains: a Partial Survey ⋮ The Dirichlet problem for higher order equations in composition form ⋮ A bilinear estimate for biharmonic functions in Lipschitz domains ⋮ The regularity of a semilinear elliptic system with quadratic growth of gradient ⋮ Polyharmonic capacity and Wiener test of higher order ⋮ Weak maximum principle for biharmonic equations in quasiconvex Lipschitz domains ⋮ Boundedness of the Hessian of a Biharmonic Function in a Convex Domain ⋮ Regularity of solutions to the polyharmonic equation in general domains ⋮ The \(L^{p}\) boundary value problems on Lipschitz domains ⋮ Optimal estimates for the inhomogeneous problem for the bi-Laplacian in three-dimensional Lipschitz domains ⋮ Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation ⋮ The 𝐿^{𝑝} regularity problem on Lipschitz domains ⋮ Boundary-value Problems for Higher-order Elliptic Equations in Non-smooth Domains ⋮ The \(L^p\) regularity problem for the Stokes system on Lipschitz domains

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