Dirac-harmonic equations for differential forms

DOI10.1016/j.na.2015.03.021zbMath1325.58011OpenAlexW2041372903MaRDI QIDQ2349029

Bing Liu, Shusen Ding

Publication date: 16 June 2015

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2015.03.021

zbMATH Keywords

a priori estimatesdifferential formsnorm inequalitiesA-harmonic equationsDirac-harmonic equationHodge-Dirac-operator

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Equations involving nonlinear operators (general) (47J05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Elliptic equations on manifolds, general theory (58J05) Differential forms in global analysis (58A10) Representations of solutions to partial differential equations (35C99)

Related Items (8)

Higher integrability of Green's operator and homotopy operator ⋮ Qualitative analysis of very weak solutions to Dirac-harmonic equations ⋮ On weak solutions to Dirac-harmonic equations for differential forms ⋮ Integral Norm Inequalities for Various Operators on Differential Forms ⋮ Norm Inequalities for Singular Integrals Related to Operators and Dirac-Harmonic Equations ⋮ Estimates for Lipschitz and BMO norms of operators on differential forms ⋮ The higher integrability of commutators of Calderón-Zygmund singular integral operators on differential forms ⋮ Characterization of the non-homogenous Dirac-harmonic equation

Cites Work

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• Hardy-Littlewood theorems for \(A\)-harmonic tensors
• Integral estimates for null Lagrangians
• Variational integrals of a class of nonhomogeneous \(\mathcal{A}\)-harmonic equations
• Poincaré inequalities for composition operators with \(L^\varphi -\)norm
• Some weighted norm estimates for the composition of the homotopy and Green's operator
• Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation
• Global Poincaré inequalities for Green's operator applied to the solutions of the nonhomogeneous \(A\)-harmonic equation
• Generalized Poincaré inequalities for solutions to the \(A\)-harmonic equation in certain domains
• Weighted integral inequalities for solutions of the \(A\)-harmonic equation
• Norm inequalities for composition of the Dirac and Green's operators
• Norm comparison estimates for the composite operator
• Inequalities for Differential Forms
• Hardy-Littlewood inequality for quasiregular mappings in certain domains in R^n
• Weighted Caccioppoli-type estimates and weak reverse Hölder inequalities for 𝐴-harmonic tensors

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