Definition and properties of supersolutions to the porous medium equation

DOI10.1515/CRELLE.2008.035zbMath1188.35109MaRDI QIDQ3524808

Peter Lindqvist, Juha Kinnunen

Publication date: 15 September 2008

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

zbMATH Keywords

comparison principlesharp summability exponentsspatial Sobolev gradient

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Degenerate parabolic equations (35K65) A priori estimates in context of PDEs (35B45)

Related Items (20)

The equivalence of weak and very weak supersolutions to the porous medium equation ⋮ Regularity of weak supersolutions to elliptic and parabolic equations: lower semicontinuity and pointwise behavior ⋮ Weak Harnack estimates for supersolutions to doubly degenerate parabolic equations ⋮ Supercaloric functions for the porous medium equation ⋮ Lower semicontinuous obstacles for the porous medium equation ⋮ Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic p-Laplace equations ⋮ Unbounded supersolutions of some quasilinear parabolic equations: a dichotomy ⋮ Regularity in parabolic systems with continuous coefficients ⋮ The porous medium equation with measure data ⋮ Continuity up to the boundary for obstacle problems to porous medium type equations ⋮ The fast diffusion equation with measure data ⋮ Regularity results for a class of doubly nonlinear very singular parabolic equations ⋮ The obstacle problem for the porous medium equation ⋮ Perron's method for the porous medium equation ⋮ Erratum to: ``Definition and properties of supersolutions to the porous medium equation ⋮ Boundary regularity for the porous medium equation ⋮ Regularity of weak solutions and supersolutions to the porous medium equation ⋮ On the Hölder regularity for obstacle problems to porous medium type equations ⋮ Some existence and regularity results for porous media and fast diffusion equations with a gradient term ⋮ Lower semicontinuity of weak supersolutions to the porous medium equation

Cites Work

• Pointwise behaviour of semicontinuous supersolutions to a quasilinear parabolic equation
• Intrinsic Harnack type inequalities for solutions of certain degenerate parabolic equations
• Quasilinear elliptic-parabolic differential equations
• Non-negative solutions of theo porous medium eqation
• Stabilization of solutions of a degenerate nonlinear diffusion problem

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