A new approach to absolute continuity of elliptic measure, with applications to non-symmetric equations

From MaRDI portal

Publication:1580854

Jump to:navigation, search

DOI10.1006/aima.1999.1899zbMath0958.35025OpenAlexW2068569862MaRDI QIDQ1580854

Carlos E. Kenig, Jill Pipher, Tatiana Toro, Herbert Koch

Publication date: 27 March 2001

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aima.1999.1899

zbMATH Keywords

nonsymmetric elliptic equation absolute continuity of elliptic measure

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) PDEs with low regular coefficients and/or low regular data (35R05) Second-order elliptic equations (35J15)

Related Items (77)

Uniform rectifiability implies Varopoulos extensions ⋮ Generalized Carleson perturbations of elliptic operators and applications ⋮ Carleson measure estimates and \(\varepsilon\)-approximation for bounded harmonic functions, without Ahlfors regularity assumptions ⋮ Regularity theory for solutions to second order elliptic operators with complex coefficients and the \(L^{p}\) Dirichlet problem ⋮ The Dirichlet problem for elliptic operators having a BMO anti-symmetric part ⋮ The Dirichlet and regularity problems for some second order linear elliptic systems on bounded Lipschitz domains ⋮ Square functions and the \(A_\infty\) property of elliptic measures ⋮ Layer potentials beyond singular integral operators ⋮ Uniform rectifiability from Carleson measure estimates and {\(\epsilon\)}-approximability of bounded harmonic functions ⋮ Higher-Order Elliptic Equations in Non-Smooth Domains: a Partial Survey ⋮ BMO solvability and \(A_\infty\) condition of the elliptic measures in uniform domains ⋮ Local Profiles for Elliptic Problems at Different Scales: Defects in, and Interfaces between Periodic Structures ⋮ Boundary layers, Rellich estimates and extrapolation of solvability for elliptic systems ⋮ A connection between regularity and Dirichlet problems for non-divergence elliptic equations ⋮ The \(L^p\)-solvability of the Dirichlet problem for planar elliptic equations, sharp results ⋮ The Dirichlet problem for higher order equations in composition form ⋮ A change of variable for Dahlberg-Kenig-Pipher operators ⋮ BMO solvability and the \(A_\infty\) condition for second order parabolic operators ⋮ Probabilistic representations of solutions of elliptic boundary value problem and non-symmetric semigroups ⋮ The method of layer potentials inL^pand endpoint spaces for elliptic operators withL^∞coefficients ⋮ Boundary estimates for solutions to operators of \(p\)-Laplace type with lower order terms ⋮ Elliptic equations in the plane satisfying a Carleson measure condition ⋮ On the condition for elliptic operators in 1-sided nontangentially accessible domains satisfying the capacity density condition ⋮ The Green function with pole at infinity applied to the study of the elliptic measure ⋮ On area integral estimates for solutions to parabolic systems in time-varying and non-smooth cylinders ⋮ Carleson perturbations for the regularity problem ⋮ Optimal Poisson kernel regularity for elliptic operators with Hölder continuous coefficients in vanishing chord-arc domains ⋮ Regularity and Neumann problems for operators with real coefficients satisfying Carleson conditions ⋮ Gradient estimates and the fundamental solution for higher-order elliptic systems with lower-order terms ⋮ Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets ⋮ Analyticity of layer potentials and \(L^{2}\) solvability of boundary value problems for divergence form elliptic equations with complex \(L^{\infty }\) coefficients ⋮ BMO solvability and the \(A_{\infty}\) condition for elliptic operators ⋮ The regularity problem in domains with lower dimensional boundaries ⋮ Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces ⋮ Homogenization of elliptic boundary value problems in Lipschitz domains ⋮ Boundary value problems for second-order elliptic operators with complex coefficients ⋮ The connections between Dirichlet, regularity and Neumann problems for second order elliptic operators with complex bounded measurable coefficients ⋮ Perturbations of elliptic operators in 1-sided chord-arc domains. Part II: Non-symmetric operators and Carleson measure estimates ⋮ Boundary rectifiability and elliptic operators with \(W^{1, 1}\) coefficients ⋮ $\varepsilon $-approximability of harmonic functions in $L^p$ implies uniform rectifiability ⋮ Dahlberg's theorem in higher co-dimension ⋮ Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems ⋮ Representation and uniqueness for boundary value elliptic problems via first order systems ⋮ Boundary behavior of solutions of elliptic operators in divergence form with a BMO anti-symmetric part ⋮ On domain of Poisson operators and factorization for divergence form elliptic operators ⋮ Boundary Korn inequality and Neumann problems in homogenization of systems of elasticity ⋮ Harmonic measure on sets of codimension larger than one ⋮ The Ẇ−1,p Neumann problem for higher order elliptic equations ⋮ Weighted maximal regularity estimates and solvability of non-smooth elliptic systems. I ⋮ Solvability of elliptic systems with square integrable boundary data ⋮ Non-unique solutions to boundary value problems for non-symmetric divergence form equations ⋮ The regularity and Neumann problem for non-symmetric elliptic operators ⋮ On Poisson operators and Dirichlet-Neumann maps in $H^s$ for divergence form elliptic operators with Lipschitz coefficients ⋮ Uniform rectifiability and \(\varepsilon\)-approximability of harmonic functions in \(L^p\) ⋮ Carleson measure estimates and the Dirichlet problem for degenerate elliptic equations ⋮ The Dirichlet problem in domains with lower dimensional boundaries ⋮ The \(L^p\) Dirichlet problem for second order elliptic operators and a \(p\)-adapted square function ⋮ Remark on the Helmholtz decomposition in domains with noncompact boundary ⋮ Estimates for solutions to equations of \(p\)-Laplace type in Ahlfors regular NTA-domains ⋮ Elliptic Partial Differential Equations with Almost-Real Coefficients ⋮ A new elliptic measure on lower dimensional sets ⋮ The absolute continuity of elliptic measure revisited ⋮ Elliptic measures and square function estimates on 1-sided chord-arc domains ⋮ Boundary value problems in Lipschitz domains for equations with lower order coefficients ⋮ Quantitative Fatou theorems and uniform rectifiability ⋮ 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 ⋮ Parabolic \(L^p\) Dirichlet boundary value problem and VMO-type time-varying domains ⋮ Critical perturbations for second-order elliptic operators. I: Square function bounds for layer potentials ⋮ Extrapolation of the Dirichlet problem for elliptic equations with complex coefficients ⋮ An \(L^q\) regularity condition that implies the \(A_\infty\) property of parabolic measure ⋮ 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 ⋮ On Isomorphism for the Space of Solenoidal Vector Fields and Its Application to the Incompressible Flows ⋮ Boundary-value Problems for Higher-order Elliptic Equations in Non-smooth Domains ⋮ Elliptic Theory for Sets with Higher Co-dimensional Boundaries ⋮ Boundary Value Problems for Second‐Order Elliptic Operators Satisfying a Carleson Condition

Cites Work

This page was built for publication: A new approach to absolute continuity of elliptic measure, with applications to non-symmetric equations

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:1580854&oldid=13865774"