\(L^{p(x)}(\varOmega)\)-estimates of vector fields and some applications to magnetostatics problems

DOI10.1016/J.JMAA.2011.12.029zbMath1234.35192OpenAlexW2006093698MaRDI QIDQ764927

D. Kharzeev

Publication date: 16 March 2012

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.12.029

zbMATH Keywords

variable exponent Lebesgue spacesdiv-curl estimatesHölder-type inequalitiesmagnetostatics problems

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Special properties of functions of several variables, Hölder conditions, etc. (26B35) Electro- and magnetostatics (78A30)

Related Items (12)

Modular inequalities for the maximal operator in variable Lebesgue spaces ⋮ Solutions to p(x)-Laplace type equations via nonvariational techniques ⋮ Regularity estimates for quasilinear elliptic equations with variable growth involving measure data ⋮ A damped Kačanov scheme for the numerical solution of a relaxed \(p(x)\)-Poisson equation ⋮ Fractional differentiability for elliptic measure data problems with variable exponents ⋮ On the asymptotic behaviour of a variable exponent power law magnetostatic problem ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Estimating the gradient of vector fields via div and curl in variable exponent Sobolev spaces ⋮ Multivalued elliptic operators with nonstandard growth ⋮ Unnamed Item

Cites Work

• Lebesgue and Sobolev spaces with variable exponents
• A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions
• Topology of the space \(\mathcal L^{p(t)}([0,t)\)]
• A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces
• \(L_p\)-estimates for vector fields
• AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
• Über konjugierte Exponentenfolgen
• Finite Element Methods for Maxwell's Equations
• Maximal function on generalized Lebesgue spaces L^p(⋅)
• Variable Exponent, Linear Growth Functionals in Image Restoration
• Mathematical modeling of electrorheological materials
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
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