Global higher regularity of solutions to singular \(p(x,t)\)-parabolic equations

DOI10.1016/j.jmaa.2018.05.075OpenAlexW2806719249WikidataQ59227286 ScholiaQ59227286MaRDI QIDQ1645121

Sergey Shmarev, Ivan V. Kuznetsov, Stanislav N. Antontsev

Publication date: 28 June 2018

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.2018.05.075

zbMATH Keywords

strong solutionssingular parabolic equationvariable nonlinearityhigher regularity

Mathematics Subject Classification ID

Ordinary differential equations (34-XX) Partial differential equations (35-XX)

Related Items

Nonlocal evolution equations with \(p[u(x, t)\)-Laplacian and lower-order terms] ⋮ On quasilinear anisotropic parabolic equations with time-dependent exponents ⋮ Pullback exponential attractors for second-order lattice system with nonstandard growth condition ⋮ Image denoising based on a variable spatially exponent PDE ⋮ Global existence and regularity for a pseudo-parabolic equation with \(p(x,t)\)-Laplacian ⋮ Upper semicontinuity of pullback D$\mathcal {D}$‐attractors for nonlinear parabolic equation with nonstandard growth condition ⋮ Strong solutions of evolution equations with \(p(x,t)\)-Laplacian: existence, global higher integrability of the gradients and second-order regularity ⋮ On a class of nonlocal evolution equations with the \(p [ u ( x , t ) \)-Laplace operator] ⋮ Existence of weak solutions to a certain homogeneous parabolic Neumann problem involving variable exponents and cross-diffusion ⋮ A SHOCK LAYER ARISING AS THE SOURCE TERM COLLAPSES IN THE P(X)-LAPLACIAN EQUATION ⋮ On a class of nonlocal evolution equations with the \(p[\nabla u\)-Laplace operator] ⋮ Global estimates for solutions of singular parabolic and elliptic equations with variable nonlinearity ⋮ Unnamed Item ⋮ Existence results for anisotropic quasilinear parabolic equations with time-dependent exponents and gradient term ⋮ Double-phase parabolic equations with variable growth and nonlinear sources

Cites Work

• Unnamed Item
• Higher regularity of solutions to the singular \(p\)-Laplacean parabolic system
• The one dimensional parabolic \(p(x)\)-Laplace equation
• Lebesgue and Sobolev spaces with variable exponents
• Existence theorems for solutions of parabolic equations with variable order of nonlinearity
• Degenerate parabolic equations
• Regularity of minima: an invitation to the dark side of the calculus of variations.
• Compact sets in the space \(L^ p(0,T;B)\)
• Regularity results for parabolic systems related to a class of non-Newtonian fluids.
• Elliptic partial differential equations of second order
• On the continuity of solutions of the nonhomogeneous evolution \(p(x, t)\)-Laplace equation
• Hölder estimates for parabolic \(p(x, t)\)-Laplacian systems
• On the property of higher integrability for parabolic systems of variable order of nonlinearity
• Hölder continuity of solutions of parabolic equations with variable nonlinearity exponent
• Anisotropic parabolic equations with variable nonlinearity
• The time derivative in a singular parabolic equation.
• Global gradient estimates for the parabolic \(p(x, t)\)-Laplacian equation
• Higher integrability for parabolic equations of \(p(x,t)\)-Laplacian type
• Hölder continuity of weak solutions for parabolic equations with nonstandard growh conditions
• Monotone operator theory for unsteady problems in variable exponent spaces
• On the Time Derivative in a Quasilinear Equation
• Evolution PDEs with Nonstandard Growth Conditions
• Regularity results for a class of functionals with non-standard growth
• Energy methods for free boundary problems. Applications to nonlinear PDEs and fluid mechanics
• On the evolution \(p\)-Laplacian with nonlocal memory