Weighted maximal regularity estimates and solvability of non-smooth elliptic systems. I

DOI10.1007/s00222-010-0285-4zbMath1231.35059arXiv0911.4344OpenAlexW3100105154MaRDI QIDQ533672

Pascal Auscher, Andreas Axelsson

Publication date: 4 May 2011

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.4344

zbMATH Keywords

elliptic systemsdivergence formaccretive mapCarleson normsolvability methods

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Weak solutions to PDEs (35D30) Second-order elliptic systems (35J47)

Related Items (52)

Weighted tent spaces with Whitney averages: factorization, interpolation and duality ⋮ Boundary value problems for general first-order elliptic differential operators ⋮ Conical maximal regularity for elliptic operators via Hardy spaces ⋮ The Dirichlet and regularity problems for some second order linear elliptic systems on bounded Lipschitz domains ⋮ Remarks on Maximal Regularity ⋮ Layer potentials beyond singular integral operators ⋮ Higher-Order Elliptic Equations in Non-Smooth Domains: a Partial Survey ⋮ Boundary layers, Rellich estimates and extrapolation of solvability for elliptic systems ⋮ Boundedness of single layer potentials associated to divergence form parabolic equations with complex coefficients ⋮ Finite speed of propagation and off-diagonal bounds for Ornstein-Uhlenbeck operators in infinite dimensions ⋮ On the Carleson duality ⋮ Singular integral operators on tent spaces: a Calderón-Zygmund theory and weak-type endpoint estimates ⋮ Square function and maximal function estimates for operators beyond divergence form equations ⋮ The Dirichlet problem for higher order equations in composition form ⋮ The method of layer potentials inL^pand endpoint spaces for elliptic operators withL^∞coefficients ⋮ Singular integral operators on tent spaces ⋮ Causal sparse domination of Beurling maximal regularity operators ⋮ Carleson perturbations for the regularity problem ⋮ Existence and regularity of steady-state solutions of the Navier-Stokes equations arising from irregular data ⋮ Harmonic functions with BMO traces and their limiting behaviors on metric measure spaces ⋮ Optimal Poisson kernel regularity for elliptic operators with Hölder continuous coefficients in vanishing chord-arc domains ⋮ Analyticity of layer potentials and \(L^{2}\) solvability of boundary value problems for divergence form elliptic equations with complex \(L^{\infty }\) coefficients ⋮ 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 ⋮ UMD Banach spaces and the maximal regularity for the square root of several operators ⋮ Carleson perturbations of elliptic operators on domains with low dimensional boundaries ⋮ Layer potentials and boundary value problems for elliptic equations with complex \(L^\infty\) coefficients satisfying the small Carleson measure norm condition ⋮ Representation and uniqueness for boundary value elliptic problems via first order systems ⋮ Second order elliptic equations and Hodge-Dirac operators ⋮ On domain of Poisson operators and factorization for divergence form elliptic operators ⋮ Evolution of time-harmonic electromagnetic and acoustic waves along waveguides ⋮ The Neumann problem for higher order elliptic equations with symmetric coefficients ⋮ Weighted maximal regularity estimates and solvability of non-smooth elliptic systems. I ⋮ The Dirichlet problem in domains with lower dimensional boundaries ⋮ Conical square function estimates and functional calculi for perturbed Hodge-Dirac operators in \(L^p\) ⋮ Conical stochastic maximal \(L^p\)-regularity for \(1\leqslant p<\infty\) ⋮ \(L^{2}\) solvability of boundary value problems for divergence form parabolic equations with complex coefficients ⋮ Hardy spaces for boundary value problems of elliptic systems with block structure ⋮ Stochastic maximal regularity for rough time-dependent problems ⋮ Elliptic Partial Differential Equations with Almost-Real Coefficients ⋮ Extrapolation for the \(L^p\) Dirichlet problem in Lipschitz domains ⋮ Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators ⋮ Dirichlet and Neumann boundary values of solutions to higher order elliptic equations ⋮ Critical perturbations for second-order elliptic operators. I: Square function bounds for layer potentials ⋮ Neumann functions for second order elliptic systems with measurable coefficients ⋮ The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients ⋮ The 𝐿^{𝑝} Dirichlet boundary problem for second order elliptic Systems with rough coefficients ⋮ The L^p Dirichlet and regularity problems for second order elliptic systems with application to the Lamé system ⋮ Boundary-value Problems for Higher-order Elliptic Equations in Non-smooth Domains ⋮ Square function estimates and the Kato problem for second order parabolic operators in \(\mathbb{R}^{n + 1}\) ⋮ Boundary Value Problems for Second‐Order Elliptic Operators Satisfying a Carleson Condition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• Area integral estimates for elliptic differential operators with non- smooth coefficients
• Necessary and sufficient conditions for absolute continuity of elliptic- harmonic measure
• Quadratic estimates and functional calculi of perturbed Dirac operators
• \(L^p\) regularity of the Dirichlet problem for elliptic equations with singular drift
• Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems
• On Hofmann's bilinear estimate
• The \(L^p\) Dirichlet problem for second order elliptic operators and a \(p\)-adapted square function
• Some new function spaces and their applications to harmonic analysis.
• A generalized \(H^\infty\) functional calculus for operators on subspaces of \(L^p\) and application to maximal regularity
• L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
• The theory of weights and the Dirichlet problem for elliptic equations
• Estimates of harmonic measure
• Large perturbations of elliptic operators and the solvability of the \(L^ p\) Dirichlet problem
• The Neumann problem for elliptic equations with non-smooth coefficients
• Area integral estimates for higher order elliptic equations and systems
• 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 \(\mathbb R^n\).
• Functional calculus for a class of complex elliptic operators in dimension one (and applications to some complex elliptic equations in dimension two).
• The Neumann problem for elliptic equations with nonsmooth coefficients. II
• The \(L^ p\) Dirichlet problem for divergence form elliptic operators with non-smooth coefficients
• BMO solvability and the \(A_{\infty}\) condition for elliptic operators
• A relationship between the Dirichlet and regularity problems for elliptic equations
• Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine
• The 𝐿^{𝑝} regularity problem on Lipschitz domains
• On a quadratic estimate related to the Kato conjecture and boundary value problems
• The regularity and Neumann problem for non-symmetric elliptic operators
• On the Absolute Continuity of Elliptic Measures
• Holomorphic functional calculi and sums of commuting opertors
• A Joint Functional Calculus for Sectorial Operators with Commuting Resolvents
• Non-unique solutions to boundary value problems for non-symmetric divergence form equations
• The Dirichlet problem for elliptic equations with drift terms

This page was built for publication: Weighted maximal regularity estimates and solvability of non-smooth elliptic systems. I