Abstract
A kind of supersolutions of the so-called p-parabolic equation are studied. These p-superparabolic functions are defined as lower semicontinuous functions obeying the comparison principle. Incidentally, they are precisely the viscosity supersolutions. One of our results guarantees the existence of a spatial Sobolev gradient. For p = 2 we have the supercaloric functions and the ordinary heat equation.
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Mathematics Subject Classification (2000) 35K55
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Kinnunen, J., Lindqvist, P. Pointwise behaviour of semicontinuous supersolutions to a quasilinear parabolic equation. Annali di Matematica 185, 411–435 (2006). https://doi.org/10.1007/s10231-005-0160-x
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DOI: https://doi.org/10.1007/s10231-005-0160-x