Layer potentials beyond singular integral operators

DOI10.5565/PUBLMAT_57213_08zbMath1288.31008arXiv1210.7582MaRDI QIDQ2637441

Andreas Rosén

Publication date: 11 February 2014

Published in: Publicacions Matemàtiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.7582

zbMATH Keywords

singular integral operatorfundamental solutiondouble layer potentialfunctional calculusdivergence form system

Mathematics Subject Classification ID

Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Green's functions for elliptic equations (35J08) Boundary value problems for second-order elliptic systems (35J57)

Related Items (19)

The Dirichlet and regularity problems for some second order linear elliptic systems on bounded Lipschitz domains ⋮ Higher-Order Elliptic Equations in Non-Smooth Domains: a Partial Survey ⋮ Boundedness of single layer potentials associated to divergence form parabolic equations with complex coefficients ⋮ The method of layer potentials inL^pand endpoint spaces for elliptic operators withL^∞coefficients ⋮ Gradient estimates and the fundamental solution for higher-order elliptic systems with lower-order terms ⋮ Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces ⋮ On uniqueness results for Dirichlet problems of elliptic systems without de Giorgi-Nash-Moser regularity ⋮ \(L^2\) well-posedness of boundary value problems for parabolic systems with measurable coefficients ⋮ Representation and uniqueness for boundary value elliptic problems via first order systems ⋮ The Neumann problem for higher order elliptic equations with symmetric coefficients ⋮ The Ẇ−1,p Neumann problem for higher order elliptic equations ⋮ Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients ⋮ \(L^{2}\) solvability of boundary value problems for divergence form parabolic equations with complex coefficients ⋮ Variational approach for the Stokes and Navier-Stokes systems with nonsmooth coefficients in Lipschitz domains on compact Riemannian manifolds ⋮ Hardy spaces for boundary value problems of elliptic systems with block structure ⋮ \(L^2\) estimates for commutators of the Dirichlet-to-Neumann map associated to elliptic operators with complex-valued bounded measurable coefficients on \(\mathbb{R}_+^{n+1}\) ⋮ Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators ⋮ Critical perturbations for second-order elliptic operators. I: Square function bounds for layer potentials ⋮ The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients

Cites Work

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• Weighted maximal regularity estimates and solvability of non-smooth elliptic systems. I
• Analyticity of layer potentials and \(L^{2}\) solvability of boundary value problems for divergence form elliptic equations with complex \(L^{\infty }\) coefficients
• Solvability of elliptic systems with square integrable boundary data
• A new approach to absolute continuity of elliptic measure, with applications to non-symmetric equations
• The solution of the Kato square root problem for second order elliptic operators on \(\mathbb R^n\).
• The Green function estimates for strongly elliptic systems of second order
• Non-unique solutions to boundary value problems for non-symmetric divergence form equations
• Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators

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