Perturbation theory for solutions to second order elliptic operators with complex coefficients and the \(L^p\) Dirichlet problem

DOI10.1007/s10114-019-8214-yzbMath1422.35035arXiv1805.08614OpenAlexW2945332856WikidataQ127816572 ScholiaQ127816572MaRDI QIDQ2311716

Jill Pipher, Martin Dindoš

Publication date: 4 July 2019

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.08614

zbMATH Keywords

Dirichlet problemperturbationsecond order elliptic operators in divergence form

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25)

Related Items

A survey of functional and Lp-dissipativity theory, Bilinear embedding for divergence-form operators with complex coefficients on irregular domains, The functional dissipativity of certain systems of partial differential equations, Criterion for the functional dissipativity of the Lamé operator, Criterion for the functional dissipativity of second order differential operators with complex coefficients, Critical perturbations for second-order elliptic operators. I: Square function bounds for layer potentials, The L^p Dirichlet and regularity problems for second order elliptic systems with application to the Lamé system

Cites Work

• Harmonic analysis on 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
• The \(L^{p}\) Dirichlet problem for second-order, non-divergence form operators: solvability and perturbation results
• Solvability of elliptic systems with square integrable boundary data
• \(L^p\) regularity of the Dirichlet problem for elliptic equations with singular drift
• Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems
• The \(L^p\) Dirichlet problem for second order elliptic operators and a \(p\)-adapted square function
• The theory of weights and the Dirichlet problem for elliptic equations
• The Neumann problem for elliptic equations with non-smooth coefficients
• Regularity theory for solutions to second order elliptic operators with complex coefficients and the \(L^{p}\) Dirichlet problem
• The solution of the Kato square root problem for second order elliptic operators on \(\mathbb R^n\).
• \(L^p\) bounds for Riesz transforms and square roots associated to second order elliptic operators
• The \(L^ p\) Dirichlet problem for small perturbations of the Laplacian
• Convexity of power functions and bilinear embedding for divergence-form operators with complex coefficients
• The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients
• Criterion for the \(L^p\)-dissipativity of second order differential operators with complex coefficients
• Perturbations of elliptic operators in chord arc domains
• On the Absolute Continuity of Elliptic Measures
• Perturbation and Solvability of Initial L^p Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains
• The 𝐿^{𝑝} Dirichlet boundary problem for second order elliptic Systems with rough coefficients