Hölder regularity and Harnack inequality for degenerate parabolic equations related to Caffarelli-Kohn-Nirenberg inequalities

DOI10.1016/j.na.2004.03.024zbMath1053.35070OpenAlexW2091899640MaRDI QIDQ1881337

Ireneo Peral Alonso, Boumediene Abdellaoui

Publication date: 4 October 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2004.03.024

zbMATH Keywords

blow-upquasilinear parabolic equationsHardy-Sobolev inequalities

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Degenerate parabolic equations (35K65) Degenerate elliptic equations (35J70) Initial value problems for second-order parabolic equations (35K15)

Related Items (11)

On the dynamics of a strongly singular parabolic equation ⋮ Pointwise estimates of solutions to the weighted porous medium equation and the fast diffusion one via weighted Riesz potentials ⋮ Fine properties of solutions to the Cauchy problem for a fast diffusion equation with Caffarelli-Kohn-Nirenberg weights ⋮ Harnack estimates for a quasi-linear parabolic equation with a singular weight ⋮ Quantitative a priori estimates for fast diffusion equations with Caffarelli-Kohn-Nirenberg weights. Harnack inequalities and Hölder continuity ⋮ Ireneo peral: forty years as mentor ⋮ A Harnack inequality for weighted degenerate parabolic equations ⋮ The interface blow-up phenomenon and local estimates for doubly degenerate parabolic equations ⋮ Local Hölder continuity of nonnegative weak solutions of degenerate parabolic equations ⋮ Local boundedness of local weak solutions for doubly degenerate parabolic systems with singular weights ⋮ On the continuity of solutions of the equations of a porous medium and the fast diffusion with weighted and singular lower-order terms

Cites Work

• Degenerate parabolic equations
• Intrinsic Harnack type inequalities for solutions of certain degenerate parabolic equations
• Existence and nonexistence results for a class of linear and semilinear parabolic equations related to some Caffarelli-Kohn-Nirenberg inequalities
• Nonnegative solutions of degenerating quasilinear parabolic equations with measurable coefficients
• A Harnack inequality for degenerate parabolic equations
• Harnack Estimates and Extinction Profile for Weak Solutions of Certain Singular Parabolic Equations
• Mean value and Harnack inequalities for degenerate parabolic equations
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