6533b824fe1ef96bd1280aed

RESEARCH PRODUCT

Lower semicontinuity of weak supersolutions to the porous medium equation

Benny AvelinTeemu Lukkari

subject

Degenerate diffusion35K55 31C45Applied MathematicsGeneral MathematicsMathematical analysista111Mathematics::Analysis of PDEscomparison principlelower semicontinuitysupersolutionsMathematics - Analysis of PDEsporous medium equationFOS: MathematicsPorous mediumdegenerate diffusionSign (mathematics)MathematicsAnalysis of PDEs (math.AP)

description

Weak supersolutions to the porous medium equation are defined by means of smooth test functions under an integral sign. We show that nonnegative weak supersolutions become lower semicontinuous after redefinition on a set of measure zero. This shows that weak supersolutions belong to a class of supersolutions defined by a comparison principle.

yearjournalcountryeditionlanguage
2013-12-10
https://dx.doi.org/10.48550/arxiv.1312.2820