Optimal estimates for the inhomogeneous problem for the bi-Laplacian in three-dimensional Lipschitz domains

DOI10.1007/s10958-010-0187-4zbMath1238.35024OpenAlexW2094879775MaRDI QIDQ549420

Yong-Cai Geng, Sumit K. Garg

Publication date: 18 July 2011

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-010-0187-4

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items

Nonlinear approximation of 3D smectic liquid crystals: sharp lower bound and compactness, 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, Regularity of solutions to the polyharmonic equation in general domains, Multilayer potentials for higher-order systems in rough domains, The Ẇ−1,p Neumann problem for higher order elliptic equations, Boundary value problems for the Laplacian in convex and semiconvex domains, Trace and extension theorems relating Besov spaces to weighted averaged Sobolev spaces, Transmission boundary problems for Dirac operators on Lipschitz domains and applications to Maxwell’s and Helmholtz’s equations, 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

• Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation
• 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
• Potential techniques for boundary value problems on \(C^1\)-domains
• The inhomogeneous Dirichlet problem for \(\Delta^2\) in Lipschitz domains
• Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains
• A maximum principle for biharmonic functions in Lipschitz and \(C^ 1\) domains
• Hölder inequalities and sharp embeddings in function spaces of \(B_{pq}^ s\) and \(F_{pq}^ s\) type
• Area integral estimates for higher order elliptic equations and systems
• 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
• Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers.
• The inhomogeneous Dirichlet problem in Lipschitz domains
• Maximum principles for the polyharmonic equation on Lipschitz domains
• \(H^ p\) theory on a smooth domain in \(\mathbb{R}^ N\) and elliptic boundary value problems
• The \(L^{p}\) boundary value problems on Lipschitz domains
• Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains
• The biharmonic Neumann problem in Lipschitz domains
• On estimates of biharmonic functions on Lipschitz and convex domains
• The Poisson problem for the exterior derivative operator with Dirichlet boundary condition in nonsmooth domains
• \(H^p\) spaces of several variables
• $L^q$-estimates for Green potentials in Lipschitz domains.
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• On Restrictions and Extensions of the Besov and Triebel-Lizorkin Spaces with Respect to Lipschitz Domains
• Dirichlet Problem in Lipschitz Domains with BMO Data
• 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
• A nonlinear Fokker-Planck equation modelling the approach to thermal equilibrium in a homogeneous plasma
• Hardy spaces, BMO, and boundary value problems for the Laplacian on a smooth domain in 𝐑^{𝐍}
• The dual of Hardy spaces on a bounded domain in ℝ n
• Potential theory on lipschitz domains in riemannian manifolds: hölder continuous metric tensors
• Geometry and stability of bubbles with gravity
• Regular Elliptic Boundary Value Problems in Besov‐Triebel‐Lizorkin Spaces
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