\(A\)-harmonic equations and the Dirac operator

DOI10.1155/2010/124018zbMath1207.35144OpenAlexW2154883910WikidataQ59254738 ScholiaQ59254738MaRDI QIDQ978410

Craig A. Nolder

Publication date: 24 June 2010

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/233310

zbMATH Keywords

Clifford algebraCaccioppoli estimateDirac system\(A\)-harmonic equation\(A\)-Dirac equation

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) PDEs in connection with quantum mechanics (35Q40) Other generalizations of analytic functions (including abstract-valued functions) (30G30)

Related Items (20)

Lipschitz and BMO norm inequalities for the composition operator on differential forms ⋮ Convergence of very weak solutions to \(A\)-Dirac equations in Clifford analysis ⋮ Local distortion of M-conformal mappings ⋮ Higher integrability of iterated operators on differential forms ⋮ Clifford valued weighted variable exponent spaces with an application to obstacle problems ⋮ Stability of weak solutions to obstacle problem in Clifford analysis ⋮ Properties of solutions to A-harmonic system and A-Dirac system ⋮ On weak solutions to Dirac-harmonic equations for differential forms ⋮ Variational integral and some inequalities of a class of quasilinear elliptic system ⋮ Nonlinear parabolic systems in Clifford type analysis ⋮ Hodge decomposition of variable exponent spaces of Clifford-valued functions and applications to Dirac and Stokes equations ⋮ Navier-Stokes equations with variable viscosity in variable exponent spaces of Clifford-valued functions ⋮ The existence of weak solutions to non-homogeneous \(A\)-Dirac equations with Dirichlet boundary data ⋮ The stationary Navier-Stokes equations in variable exponent spaces of Clifford-valued functions ⋮ Weak and strong type estimates for multilinear Calderón-Zygmund operators on differential forms ⋮ Weak solution for \(A\)-Dirac equations in Clifford analysis ⋮ Dirac-harmonic equations for differential forms ⋮ Existence of stationary states for \(A\)-Dirac equations with variable growth ⋮ On a eigenvalue problem involving Dirac operator ⋮ Regularity theory on \(A\)-harmonic system and \(A\)-Dirac system

Cites Work

• Nonlinear \(A\)-Dirac equations
• \(p\)-Dirac operators
• Dirac-harmonic maps
• Jump problem and removable singularities for monogenic functions
• Removable singularities for analytic or subharmonic functions
• Removability theorems for solutions of degenerate elliptic partial differential equations
• Nonlinear Dirac equations on Riemann surfaces
• Regularity theorems and energy identities for Dirac-harmonic maps
• Removable sets for continuous solutions of quasilinear elliptic equations
• A remark on nonlinear Dirac equations
• Regularity of Dirac-Harmonic Maps
• Mean Oscillation Over Cubes and Holder Continuity
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