Hodge decomposition of variable exponent spaces of Clifford-valued functions and applications to Dirac and Stokes equations

DOI10.1016/j.camwa.2015.05.020zbMath1443.30016OpenAlexW579208708MaRDI QIDQ2006189

Binlin Zhang, Yongqiang Fu, Vicenţiu D. Rădulescu

Publication date: 8 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2015.05.020

zbMATH Keywords

Clifford analysisStokes equationvariable exponent\(A\)-Dirac equation\(L^{p(x)}\)-decomposition

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Functions of hypercomplex variables and generalized variables (30G35) PDEs in connection with quantum mechanics (35Q40)

Related Items (6)

Linear stability of blowup solution of incompressible Keller-Segel-Navier-Stokes system ⋮ Artificial boundary condition for one-dimensional nonlinear Schrödinger problem with Dirac interaction: existence and uniqueness results ⋮ Dirichlet type problems for Dunkl-Poisson equations ⋮ Navier-Stokes equations with variable viscosity in variable exponent spaces of Clifford-valued functions ⋮ A new variable exponent Picone identity and applictions ⋮ Existence of stationary states for \(A\)-Dirac equations with variable growth

Cites Work

• Clifford valued weighted variable exponent spaces with an application to obstacle problems
• Nonlinear \(A\)-Dirac equations
• Campanato estimates for the generalized Stokes system
• Lebesgue and Sobolev spaces with variable exponents
• BMO estimates for the \(p\)-Laplacian
• \(p\)-Dirac operators
• An introduction to Sobolev spaces and interpolation spaces
• Overview of differential equations with non-standard growth
• \(A\)-harmonic equations and the Dirac operator
• The principle of concentration compactness in \(L^{p(x)}\) spaces and its application
• Functional analysis, Sobolev spaces and partial differential equations
• On the modeling of electrorheological materials
• Sur l'analysis situs des variétés à \(n\) dimensions
• Weak solution for obstacle problem with variable growth
• Quaternionic analysis and elliptic boundary value problems
• \(L^q\) theory for a generalized Stokes system
• On a direct decomposition of the space \({\mathcal L}_p(\Omega)\)
• Nonlinear elliptic equations with variable exponent: old and new
• Espaces d'interpolation et théorème de Soboleff
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• The Stokes and Poisson problem in variable exponent spaces
• Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension
• A Dirichlet Problem for Harmonic Functionals, with Applications to Analytic Varities
• Variational problems in Clifford analysis
• Elliptic boundary value problems of fluid dynamics over unbounded domains
• Partial Differential Equations with Variable Exponents
• Weak solutions for elliptic systems with variable growth in Clifford analysis
• A Remark on the Coupling of Gravitation and Electron
• Doubts and hopes in quantumelectrodynamics
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Hodge decomposition of variable exponent spaces of Clifford-valued functions and applications to Dirac and Stokes equations