Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients

DOI10.1007/s00229-016-0839-xzbMath1358.35035arXiv1409.7600OpenAlexW1623038730MaRDI QIDQ728465

Ariel Barton

Publication date: 20 December 2016

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.7600

zbMATH Keywords

fundamental solutiongradient estimatesrough coefficientshigher-order elliptic system

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Higher-order elliptic systems (35J48)

Related Items (18)

Maximal function characterizations of Hardy spaces associated to homogeneous higher order elliptic operators ⋮ Higher-Order Elliptic Equations in Non-Smooth Domains: a Partial Survey ⋮ Combined effects of homogenization and singular perturbations: Quantitative estimates ⋮ \(\mathcal {R}\)-sectoriality of higher-order elliptic systems on general bounded domains ⋮ Gradient estimates and the fundamental solution for higher-order elliptic systems with lower-order terms ⋮ Local Hardy spaces associated with inhomogeneous higher order elliptic operators ⋮ Convergence rates and interior estimates in homogenization of higher order elliptic systems ⋮ Weak maximum principle for biharmonic equations in quasiconvex Lipschitz domains ⋮ On uniqueness results for Dirichlet problems of elliptic systems without de Giorgi-Nash-Moser regularity ⋮ Asymptotic Expansions for Higher Order Elliptic Equations with an Application to Quantitative Photoacoustic Tomography ⋮ Uniform boundary estimates in homogenization of higher-order elliptic systems ⋮ Regularity for free interface variational problems in a general class of gradients ⋮ The Neumann problem for higher order elliptic equations with symmetric coefficients ⋮ The Ẇ−1,p Neumann problem for higher order elliptic equations ⋮ Tent space well-posedness for parabolic Cauchy problems with rough coefficients ⋮ Trace and extension theorems relating Besov spaces to weighted averaged Sobolev spaces ⋮ Dirichlet and Neumann boundary values of solutions to higher order elliptic equations ⋮ Convergence rates in almost-periodic homogenization of higher-order elliptic systems

Cites Work

• Unnamed Item
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• Unnamed Item
• Multi-layer potentials and boundary problems for higher-order elliptic systems in Lipschitz domains
• Global pointwise estimates for Green's matrix of second order elliptic systems
• Global estimates for Green's matrix of second order parabolic systems with application to elliptic systems in two dimensional domains
• To the theory of the Dirichlet and Neumann problems for strongly elliptic systems in Lipschitz domains
• An irregular complex valued solution to a scalar uniformly elliptic equation
• The Dirichlet problem in Lipschitz domains for higher order elliptic systems with rough coefficients
• Adjoint boundary value problems for the biharmonic equation on \(C^ 1\) domains in the plane
• The Green matrix for strongly elliptic systems of second order with continuous coefficients
• The Green function for uniformly elliptic equations
• Quasiconformal mappings and extendability of functions in Sobolev spaces
• A survey on explicit representation formulae for fundamental solutions of linear partial differential operators
• Heat kernels of second order complex elliptic operators and applications
• Equivalence between regularity theorems and heat kernel estimates for higher-order elliptic operators and systems under divergence form
• The Kato square root problem for higher order elliptic operators and systems on \(\mathbb{R}^n\)
• The Wiener test for higher order elliptic equations.
• Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators
• Estimates for Green's matrices of elliptic systems by \(L^ p\) theory
• A family of fundamental solutions of elliptic partial differential operators with real constant coefficients
• The Green function estimates for strongly elliptic systems of second order
• The biharmonic Neumann problem in Lipschitz domains
• Error-bounds for finite element method
• \(H^p\) spaces of several variables
• Layer potentials beyond singular integral operators
• Boundedness of the Hessian of a Biharmonic Function in a Convex Domain
• Green’s matrices of second order elliptic systems with measurable coefficients in two dimensional domains
• Pointwise estimates for the polyharmonic Green function in general domains
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• On Harnack's theorem for elliptic differential equations
• Square function estimates on layer potentials for higher‐order elliptic equations
• Boundary Coerciveness and the Neumann Problem for 4th Order Linear Partial Differential Operators
• On Fundamental Solutions of Elliptic Equations
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
• The Green formula and layer potentials

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