Nonlinear \(A\)-Dirac equations

DOI10.1007/s00006-010-0253-5zbMath1253.30073OpenAlexW1978919016MaRDI QIDQ451099

Craig A. Nolder

Publication date: 21 September 2012

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00006-010-0253-5

zbMATH Keywords

Caccioppoli estimateglobal integrabilitynonlinear Dirac equations

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Quasilinear elliptic equations (35J62) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (19)

Convergence of very weak solutions to \(A\)-Dirac equations in Clifford analysis ⋮ Local distortion of M-conformal mappings ⋮ 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 ⋮ Derivations and linear connections on Clifford vector bundles ⋮ Variational integral and some inequalities of a class of quasilinear elliptic system ⋮ Nonlinear parabolic systems in Clifford type analysis ⋮ Weak solutions for elliptic systems with variable growth in Clifford analysis ⋮ \(A\)-harmonic operator in the Dirac system ⋮ 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 ⋮ \(A\)-harmonic equations and the Dirac operator ⋮ 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 solution for \(A\)-Dirac equations in Clifford analysis ⋮ Existence of stationary states for \(A\)-Dirac equations with variable growth ⋮ Regularity theory on \(A\)-harmonic system and \(A\)-Dirac system

Cites Work

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• \(p\)-Dirac operators
• Dirac-harmonic maps
• Construction of singular solutions to the p-harmonic equation and its limit equation for \(p=\infty\)
• Whitney cubes, p-capacity, and Minkowski content
• On certain p-harmonic functions in the plane
• Global integrability theorems for \(A\)-harmonic tensors
• Quasiconformal mappings and global integrability of the derivative
• Nonlinear Dirac equations on Riemann surfaces
• Regularity theorems and energy identities for Dirac-harmonic maps
• The radial variation of analytic functions
• A remark on nonlinear Dirac equations
• Regularity of Dirac-Harmonic Maps
• Global integrability of the gradients of solutions to partial differential equations
• Mean Oscillation Over Cubes and Holder Continuity

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