Pointwise estimates for solutions to the porous medium equation with measure as a forcing term

DOI10.1007/s11856-012-0098-9zbMath1357.35198OpenAlexW1968382853MaRDI QIDQ1955739

Vitali Liskevich, Igor I. Skrypnik

Publication date: 18 June 2013

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-012-0098-9

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic equations (35K20) Flows in porous media; filtration; seepage (76S05) Weak solutions to PDEs (35D30) Quasilinear parabolic equations (35K59) PDEs with measure (35R06)

Related Items (11)

Degenerate and Singular Porous Medium Type Equations with Measure Data ⋮ Riesz potentials and pointwise estimates of solutions to anisotropic porous medium equation ⋮ Stability properties of Radon measure-valued solutions for a class of nonlinear parabolic equations under Neumann boundary conditions ⋮ Sharp boundedness and continuity results for the singular porous medium equation ⋮ Pointwise estimates of solutions to the weighted porous medium equation and the fast diffusion one via weighted Riesz potentials ⋮ Continuity estimates for porous medium type equations with measure data ⋮ Pointwise estimates via parabolic potentials for a class of doubly nonlinear parabolic equations with measure data ⋮ Local subestimates of solutions to double-phase parabolic equations via nonlinear parabolic potentials ⋮ On the continuity of solutions of the equations of a porous medium and the fast diffusion with weighted and singular lower-order terms ⋮ Harnack estimates at large: sharp pointwise estimates for nonnegative solutions to a class of singular parabolic equations ⋮ Removable singularities of quasilinear parabolic equations with coefficients from Kato-type classes

Cites Work

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• Degenerate diffusions. Initial value problems and local regularity theory
• Harnack inequality and continuity of solutions to quasi-linear degenerate parabolic equations with coefficients from Kato-type classes
• The Wiener test and potential estimates for quasilinear elliptic equations
• Gradient estimates via non-linear potentials
• Harnack's Inequality for Degenerate and Singular Parabolic Equations
• Potential Estimates for Quasi-Linear Parabolic Equations

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