Existence and nonexistence results for a class of linear and semilinear parabolic equations related to some Caffarelli-Kohn-Nirenberg inequalities

DOI10.4171/JEMS/4zbMath1059.35062OpenAlexW2022394700MaRDI QIDQ1432720

Boumediene Abdellaoui, Eduardo Colorado, Ireneo Peral Alonso

Publication date: 15 June 2004

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jems/4

zbMATH Keywords

Harnack inequalityspectral instantaneous and complete blow-up

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Degenerate parabolic equations (35K65) Degenerate elliptic equations (35J70)

Related Items (13)

Some remarks on elliptic problems with critical growth in the gradient ⋮ Hölder regularity and Harnack inequality for degenerate parabolic equations related to Caffarelli-Kohn-Nirenberg inequalities ⋮ Stability analysis for a family of degenerate semilinear parabolic problems ⋮ Optimal results for parabolic problems arising in some physical models with critical growth in the gradient respect to a Hardy potential ⋮ On the dynamics of a strongly singular parabolic equation ⋮ Summability and existence results for quasilinear parabolic equations with Hardy potential term ⋮ Nonlinear degenerate parabolic equations with singular coefficients for Greiner vector fields ⋮ Regularity and nonuniqueness results for parabolic problems arising in some physical models, having natural growth in the gradient ⋮ Ireneo peral: forty years as mentor ⋮ Quasilinear parabolic and elliptic equations with singular potentials ⋮ Quasilinear elliptic equations with Neumann boundary and singularity ⋮ Competition reaction-absorption in some elliptic and parabolic problems related to the Caffarelli-Kohn-Nirenberg inequalities ⋮ A remark on the existence properties of a semilinear heat equation involving a Hardy-Leray potential

Cites Work

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• Uniqueness of solutions of the initial-value problem for \(u_t- \Delta\varphi (u)=0\)
• On quasilinear elliptic equations related to some Caffarelli-Kohn-Nirenberg inequalities
• Existence and nonexistence results for quasilinear elliptic equations involving the \(p\)-Laplacian with a critical potential
• The Heat Equation with a Singular Potential
• Some results for semilinear elliptic equations with critical potential
• Renormalised solutions of nonlinear parabolic problems with L¹ data: existence and uniqueness
• Global Behavior of the Cauchy Problem for Some Critical Nonlinear Parabolic Equations

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