The Green Function for Elliptic Systems in Two Dimensions

DOI10.1080/03605302.2013.814668zbMath1279.35021arXiv1205.1089OpenAlexW2056121942MaRDI QIDQ2855222

Seick Kim, Justin L. Taylor, Russell M. Brown

Publication date: 24 October 2013

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.1089

zbMATH Keywords

BMOmixed boundary conditionsGreen function

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) (H^p)-spaces (42B30) Green's functions for elliptic equations (35J08) Harmonic analysis and PDEs (42B37)

Related Items (18)

Pointwise a posteriori error analysis of a finite element method for the Signorini problem ⋮ The mixed problem for the Lamé system in two dimensions ⋮ Singularity extraction for elliptic equations with coefficients with jumps and Dirac sources ⋮ Stochastic homogenization of Gaussian fields on random media ⋮ Pointwise a posteriori error control of discontinuous Galerkin methods for unilateral contact problems ⋮ Uniform estimates of resolvents in homogenization theory of elliptic systems ⋮ Structure of Green's function of elliptic equations and helical vortex patches for 3D incompressible Euler equations ⋮ Homogenization theory of elliptic system with lower order terms for dimension two ⋮ The Stokes paradox in inhomogeneous elastostatics ⋮ Heat kernel for the elliptic system of linear elasticity with boundary conditions ⋮ Optimal Morrey estimate for parabolic equations in divergence form via Green's functions ⋮ A heterogeneous stochastic FEM framework for elliptic PDEs ⋮ Green's Function for Nondivergence Elliptic Operators in Two Dimensions ⋮ Heat kernel bounds for elliptic partial differential operators in divergence form with Robin-type boundary conditions ⋮ The plane exterior boundary-value problem for nonhomogeneous fluids ⋮ The Green function for the mixed problem for the linear Stokes system in domains in the plane ⋮ Neumann functions for second order elliptic systems with measurable coefficients ⋮ Asymptotic self-similarity in diffusion equations with nonconstant radial limits at infinity

Cites Work

• The mixed problem for the Lamé system in two dimensions
• Well-posedness and regularity for the elasticity equation with mixed boundary conditions on polyhedral domains and domains with cracks
• A \(W^{1,p}\)-estimate for solutions to mixed boundary value problems for second order elliptic differential equations
• The Green function for uniformly elliptic equations
• Continuity of solutions of uniformly elliptic equations in \(\mathbb{R}^ 2\)
• The Neumann problem for elliptic equations with non-smooth coefficients
• Heat kernels of second order complex elliptic operators and applications
• Estimates for Green's matrices of elliptic systems by \(L^ p\) theory
• The mixed problem for the Laplacian in Lipschitz domains
• Problemi al contorno ellittici, con dati discontinui, dotati di soluzioni hölderiane
• The L\(^p\)-integrability of the partial derivatives of a quasiconformal mapping
• The mixed problem in Lipschitz domains with general decompositions of the boundary
• On the Regularity of Green Functions in Lipschitz Domains
• Green’s matrices of second order elliptic systems with measurable coefficients in two dimensional domains
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• Extensions of Hardy spaces and their use in analysis
• Elliptic Partial Differential Equations of Second Order
• The dual of Hardy spaces on a bounded domain in ℝ n

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