The inhomogeneous Dirichlet problem for \(\Delta^2\) in Lipschitz domains
From MaRDI portal
Publication:1273946
DOI10.1006/jfan.1998.3300zbMath0934.35038OpenAlexW2029083866MaRDI QIDQ1273946
Jill Pipher, Vilhelm Adolfsson
Publication date: 9 February 2000
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jfan.1998.3300
Nonlinear boundary value problems for linear elliptic equations (35J65) Boundary value problems for higher-order elliptic equations (35J40)
Related Items
Spectral theory for perturbed Krein Laplacians in nonsmooth domains, Higher-Order Elliptic Equations in Non-Smooth Domains: a Partial Survey, Area integral estimates for higher order elliptic equations and systems, The inhomogeneous Dirichlet problem for the Stokes system in Lipschitz domains with unit normal close to VMO, The Dirichlet problem for higher order equations in composition form, A bilinear estimate for biharmonic functions in Lipschitz domains, The correction operator for the canonical interpolation operator of the Adini element and the lower bounds of eigenvalues, The maximum principle of Alexandrov for very weak solutions, Boundedness of the Hessian of a Biharmonic Function in a Convex Domain, Regularity of solutions to the polyharmonic equation in general domains, A \(C^0\)-weak Galerkin finite element method for the biharmonic equation, To the theory of the Dirichlet and Neumann problems for strongly elliptic systems in Lipschitz domains, Multilayer potentials for higher-order systems in rough domains, Optimal estimates for the inhomogeneous problem for the bi-Laplacian in three-dimensional Lipschitz domains, A Survey on the Krein–von Neumann Extension, the Corresponding Abstract Buckling Problem, and Weyl-type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains, The Dirichlet problem in Lipschitz domains for higher order elliptic systems with rough coefficients, Weighted Sobolev Space Estimates for a Class of Singular Integral Operators, Trace and extension theorems relating Besov spaces to weighted averaged Sobolev spaces, Remarks on potential spaces and Besov spaces in a Lipschitz domain and on Whitney arrays on its boundary, The spectrum asymptotics for the Dirichlet problem in the case of the biharmonic operator in a domain with highly indented boundary, The minimal conforming $H^k$ finite element spaces on $R^n$ rectangular grids, Dirichlet and Neumann boundary values of solutions to higher order elliptic equations, The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations, Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem, Boundary-value Problems for Higher-order Elliptic Equations in Non-smooth Domains, Recent progress in elliptic equations and systems of arbitrary order with rough coefficients in Lipschitz domains
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The \(L^ p\)-integrability of Green's functions and fundamental solutions for elliptic and parabolic equations
- The Dirichlet problem for the biharmonic equation in a Lipschitz domain
- Hardy spaces and the Neumann problem in \(L^ p\) for Laplace's equation in Lipschitz domains
- Asymptotic properties of solutions of differential equations with simple characteristics
- A maximum principle for biharmonic functions in Lipschitz and \(C^ 1\) domains
- A computation of Green functions for the weighted biharmonic operators \(\Delta| z| ^{-2\alpha}\Delta\), with \(\alpha > -1\)
- The inhomogeneous Dirichlet problem in Lipschitz domains
- Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators
- Maximum principles for the polyharmonic equation on Lipschitz domains
- $L^q$-estimates for Green potentials in Lipschitz domains.
- Maximum theorems for solutions of higher order elliptic equations
- Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
- Weighted norm inequalities for the Lusin area integral and the nontangential maximal functions for functions harmonic in a Lipschitz domain
- Area Integral Estimates for the Biharmonic Operator in Lipschitz Domains
- The Dirichlet Problem in L p for the Biharmonic Equation on Lipschitz Domains
- Extensions of Hardy spaces and their use in analysis