Area Integral Estimates for the Biharmonic Operator in Lipschitz Domains

DOI10.2307/2001830zbMath0774.35022OpenAlexW4249146031MaRDI QIDQ3982165

Jill Pipher, Gregory C. Verchota

Publication date: 26 June 1992

Full work available at URL: https://doi.org/10.2307/2001830

zbMATH Keywords

nontangential maximal function inequalities

Mathematics Subject Classification ID

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

Related Items

Higher-Order Elliptic Equations in Non-Smooth Domains: a Partial Survey, Maximum principles for the polyharmonic equation on Lipschitz domains, Area integral estimates for higher order elliptic equations and systems, On the Dirichlet-Riquier problem for biharmonic equations, A bilinear estimate for biharmonic functions in Lipschitz domains, Higher order Poisson kernels and \(L^p\) polyharmonic boundary value problems in Lipschitz domains, Weak maximum principle for biharmonic equations in quasiconvex Lipschitz domains, Regularity of solutions to the polyharmonic equation in general domains, Optimal estimates for the inhomogeneous problem for the bi-Laplacian in three-dimensional Lipschitz domains, The biharmonic Neumann problem in Lipschitz domains, The Duals of Harmonic Bergman Spaces, The inhomogeneous Dirichlet problem for \(\Delta^2\) in Lipschitz domains, Dirichlet and Neumann boundary values of solutions to higher order elliptic equations, Boundary-value Problems for Higher-order Elliptic Equations in Non-smooth Domains

Cites Work

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• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• The Dirichlet problem for the biharmonic equation in a Lipschitz domain
• Estimates of harmonic measure
• \(H^p\) spaces of several variables
• Weighted norm inequalities for the Lusin area integral and the nontangential maximal functions for functions harmonic in a Lipschitz domain
• The Neumann problem on Lipschitz domains
• The Dirichlet Problem in L p for the Biharmonic Equation on Lipschitz Domains
• Weighted norm inequalities for maximal functions and singular integrals
• Distribution function inequalities for the area integral