The Stokes and Poisson problem in variable exponent spaces

DOI10.1080/17476933.2010.504843zbMath1241.35157arXiv1205.3287OpenAlexW2000079062MaRDI QIDQ3093069

Lars Diening, Daniel Lengeler, Michael Ružička

Publication date: 12 October 2011

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.3287

zbMATH Keywords

energysimulationharmonic analysisStokes problemvariational integralPoisson problemfluidvariable exponent spaceregularity result

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Strong solutions to PDEs (35D35)

Related Items (17)

Boundary regularity estimates in Hölder spaces with variable exponent ⋮ \(W^{2,p(\cdot )}\)-regularity for elliptic equations in nondivergence form with BMO coefficients ⋮ Interior gradient estimate for steady flows of electrorheological fluids ⋮ Weighted \(L^{p(\cdot)}\)-regularity for fully nonlinear parabolic equations ⋮ Hodge-type decomposition for time-dependent first-order parabolic operators with non-constant coefficients: the variable exponent case ⋮ Hodge type decomposition in variable exponent spaces for the time-dependent operators: the Schrödinger case ⋮ Sharp gradient estimates for quasilinear elliptic equations with \(p(x)\) growth on nonsmooth domains ⋮ 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 ⋮ On \(W^{1,q(\cdot)}\)-estimates for elliptic equations of \(p(x)\)-Laplacian type ⋮ Variable exponent Bochner-Lebesgue spaces with symmetric gradient structure ⋮ The stationary Navier-Stokes equations in variable exponent spaces of Clifford-valued functions ⋮ Variable Lorentz estimate for conormal derivative problems of stationary Stokes system with partially BMO coefficients ⋮ Variable Lorentz estimate for stationary Stokes system with partially BMO coefficients ⋮ Optimal regularity for nonlinear elliptic equations with righthand side measure in variable exponent spaces ⋮ Nondivergence parabolic equations in weighted variable exponent spaces ⋮ Existence of stationary states for \(A\)-Dirac equations with variable growth

Cites Work

• On the modeling of electrorheological materials
• Integral operators on the halfspace in generalized Lebesgue spaces \(L^{p(\cdot)}\). I, II
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)
• Convolution and potential type operators inL^p(x)(Rⁿ)
• Calderón-Zygmund operators on generalized Lebesgue spaces Lp(⋅) and problems related to fluid dynamics
• Regularity results for a class of functionals with non-standard growth
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

This page was built for publication: The Stokes and Poisson problem in variable exponent spaces