Perron's method for the porous medium equation
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Publication:502155
DOI10.4171/JEMS/658zbMath1361.35079arXiv1401.4277MaRDI QIDQ502155
Teemu Lukkari, Juha Kinnunen, Peter Lindqvist
Publication date: 30 December 2016
Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1401.4277
Nonlinear parabolic equations (35K55) Initial-boundary value problems for second-order parabolic equations (35K20) Degenerate parabolic equations (35K65) Other generalizations (nonlinear potential theory, etc.) (31C45)
Related Items (11)
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 ⋮ Obstacle problem of a nonlinear anisotropic parabolic equation ⋮ Lower semicontinuous obstacles for the porous medium equation ⋮ Continuity up to the boundary for obstacle problems to porous medium type equations ⋮ A variational approach to doubly nonlinear equations ⋮ The obstacle problem for the porous medium equation ⋮ The obstacle problem for parabolic minimizers ⋮ Boundary regularity for the porous medium equation ⋮ Doubly nonlinear equations of porous medium type ⋮ On the Hölder regularity for obstacle problems to porous medium type equations
Cites Work
- The obstacle problem for the porous medium equation
- Non-negative solutions of theo porous medium eqation
- Hölder estimates for nonlinear degenerate parabolic sytems.
- Definition and properties of supersolutions to the porous medium equation
- Lower semicontinuity of weak supersolutions to the porous medium equation
- Viscosity solutions for quasilinear degenerate parabolic equations of porous medium type
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