Harnack estimates for non-negative weak solutions of a class of singular parabolic equations

DOI10.1007/s00229-012-0562-1zbMath1264.35065OpenAlexW2056564960MaRDI QIDQ1949798

Vincenzo Vespri, Simona Fornaro

Publication date: 17 May 2013

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-012-0562-1

zbMATH Keywords

parabolic \(p\)-Laplacian

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate parabolic equations (35K65) A priori estimates in context of PDEs (35B45)

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Pointwise estimates for the fundamental solutions of a class of singular parabolic problems, Interior Harnack estimates: the state-of-the-art for quasilinear singular parabolic equations, Unnamed Item, Regularity results for a class of doubly nonlinear very singular parabolic equations, A boundary estimate for singular parabolic diffusion equations, Harnack estimates at large: sharp pointwise estimates for nonnegative solutions to a class of singular parabolic equations

Cites Work

• Degenerate parabolic equations
• Harnack estimates for quasi-linear degenerate parabolic differential equations
• Local smoothing effects, positivity, and Harnack inequalities for the fast \(p\)-Laplacian equation
• Local clustering of the non-zero set of functions in \(W^{1,1} (E)\)
• Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations
• Higher integrability for parabolic systems of \(p\)-Laplacian type
• Harnack type estimates and Hölder continuity for non-negative solutions to certain sub-critically singular parabolic partial differential equations
• Harnack's Inequality for Degenerate and Singular Parabolic Equations
• Forward, backward and elliptic Harnack inequalities for non-negative solutions to certain singular parabolic partial differential equations