The connections between Dirichlet, regularity and Neumann problems for second order elliptic operators with complex bounded measurable coefficients
type: Item
instance of: scholarly article
title: The connections between Dirichlet, regularity and Neumann problems for second order elliptic operators with complex bounded measurable coefficients
zbMATH Open document ID: 1203.35087
author: Svitlana Mayboroda
published in: Advances in Mathematics
publication date: 2010-10-07T00:00:00Z
review text: The author shows that for general elliptic operators with complex bounded measurable coefficients, the solvability of the regularity problem does not imply the solvability of the dual Dirichlet problem, contrarily to the result by \textit{C. E. Kenig} and \textit{J. Pipher} [Invent. Math. 113, No. 3, 447--509 (1993; Zbl 0807.35030)] established for operators with real coefficients. A similar result holds for the Neumann problem.
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 5796747
zbMATH Keywords: elliptic equation
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: Neumann problem
reviewed by: Radu Precup
MaRDI profile type: Publication
full work available at URL: j.aim.2010.04.019
OpenAlex ID: W2019276535
cites work: Q4891406
cites work: Analyticity of layer potentials and \(L^{2}\) solvability of boundary value problems for divergence form elliptic equations with complex \(L^{\infty }\) coefficients
cites work: On necessary and sufficient conditions for 𝐿^{𝑝}-estimates of Riesz transforms associated to elliptic operators on ℝⁿ and related estimates
cites work: Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems
cites work: The solution of the Kato square root problem for second order elliptic operators on \(\mathbb R^n\).
cites work: Q4217284
cites work: Real interpolation of Sobolev spaces
cites work: On Certain Interpolation Spaces Related to Generalized Semi-Groups.
cites work: Weak type \((p,p)\) estimates for Riesz transforms
cites work: Q3940170
cites work: Necessary and sufficient conditions for absolute continuity of elliptic- harmonic measure
cites work: Multilinear Square Functions and Partial Differential Equations
cites work: An irregular complex valued solution to a scalar uniformly elliptic equation
cites work: Q3895987
cites work: \(L^p\) bounds for Riesz transforms and square roots associated to second order elliptic operators
cites work: Hardy and BMO spaces associated to divergence form elliptic operators
cites work: Second order elliptic operators with complex bounded measurable coefficients in $L^p$, Sobolev and Hardy spaces
cites work: Q5526485
cites work: Q4305610
cites work: A new approach to absolute continuity of elliptic measure, with applications to non-symmetric equations
cites work: The Neumann problem for elliptic equations with non-smooth coefficients
cites work: The Neumann problem for elliptic equations with nonsmooth coefficients. II
cites work: The regularity and Neumann problem for non-symmetric elliptic operators
cites work: Q3963426
cites work: Q3772766
cites work: Q5607484
DOI: 10.1016/J.AIM.2010.04.019
description: scientific article; zbMATH DE number 5796747