Pointwise estimates for the fundamental solutions of a class of singular parabolic problems

DOI10.1007/s11854-013-0034-xzbMath1282.35106OpenAlexW2064380069MaRDI QIDQ393440

Vincenzo Vespri, Stella Vernier Piro, Francesco Ragnedda

Publication date: 17 January 2014

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11854-013-0034-x

zbMATH Keywords

\(L^\infty\) coefficients

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) A priori estimates in context of PDEs (35B45) Initial value problems for second-order parabolic equations (35K15) Singular parabolic equations (35K67) Quasilinear parabolic equations with (p)-Laplacian (35K92) Heat kernel (35K08) Quasilinear parabolic equations (35K59)

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Cites Work

• Unnamed Item
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• Large time behaviour of solutions of the porous media equation with absorption
• Nonlinear potential estimates in parabolic problems
• Degenerate parabolic equations
• Large time behaviour of solutions to a class of non-autonomous, degenerate parabolic equations
• Fundamental solutions and asymptotic behaviour for the p-Laplacian equations
• Renormalized solutions of nonlinear parabolic equations with general measure data
• Harnack estimates for quasi-linear degenerate parabolic differential equations
• Monotone (nonlinear) operators in Hilbert space
• Large time behaviour of solutions of the porous medium equation in bounded domains
• Source-type solutions for equations of nonstationary filtration
• Nonlinear parabolic equations with measure data
• Harnack estimates for non-negative weak solutions of a class of singular parabolic equations
• The Asymptotic Profile of Solutions of a Class of Singular Parabolic Equations
• Harnack's Inequality for Degenerate and Singular Parabolic Equations
• Hölder estimates for nonlinear degenerate parabolic sytems.
• The Asymptotic Behavior of Gas in an n-Dimensional Porous Medium
• Uniqueness of the solutions of ut−Δϕ(u) = 0 with initial datum a measure
• Definition and existence of renormalized solutions of elliptic equations with general measure data
• Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity
• Forward, backward and elliptic Harnack inequalities for non-negative solutions to certain singular parabolic partial differential equations
• Gradient regularity for nonlinear parabolic equations