A connection between a general class of superparabolic functions and supersolutions

作者：Korte Riikka; Kuusi Tuomo; Parviainen Mikko^*

来源：Journal of Evolution Equations, 2010, 10(1): 1-20.

DOI：10.1007/s00028-009-0037-3

We show for a general class of parabolic equations that every bounded superparabolic function is a weak supersolution and, in particular, has derivatives in a Sobolev sense. To this end, we establish various comparison principles between super- and subparabolic functions, and show that a pointwise limit of uniformly bounded weak supersolutions is a weak supersolution.

• 出版日期2010-3