The evolutionary \(p(x)\)-Laplacian equation with a partial boundary value condition

DOI10.1155/2018/1237289zbMath1417.35056OpenAlexW2800104963MaRDI QIDQ1726957

Zhen Zhou, Hua-Shui Zhan

Publication date: 20 February 2019

Published in: Discrete Dynamics in Nature and Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2018/1237289

Mathematics Subject Classification ID

Non-Newtonian fluids (76A05) Initial-boundary value problems for second-order parabolic equations (35K20) Magnetohydrodynamics and electrohydrodynamics (76W05) Quasilinear parabolic equations (35K59)

Cites Work

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• The boundary value condition of an evolutionary \(p(x)\)-Laplacian equation
• Existence of solutions to an initial Dirichlet problem of evolutional \(p(x)\)-Laplace equations
• Lebesgue and Sobolev spaces with variable exponents
• Embeddings between grand, small, and variable Lebesgue spaces
• Regularity results for stationary electro-rheological fluids
• Properties of the boundary flux of a singular diffusion process
• Hölder regularity for the general parabolic \(p(x, t)\)-Laplacian equations
• Anisotropic parabolic equations with variable nonlinearity
• Evolutionary weighted \(p\)-Laplacian with boundary degeneracy
• A new kind of weak solution of non-Newtonian fluid equation
• Global gradient estimates for the parabolic \(p(x, t)\)-Laplacian equation
• On the density of smooth functions in Sobolev-Orlicz spaces
• On interior regularity of minimizers of \(p(x)\)-energy functionals
• Maximal function on generalized Lebesgue spaces L^p(⋅)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

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