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A quasi-monotonicity formula and partial regularity for borderline solutions to a parabolic equation. (English) Zbl 1213.35177

A quasi-monotonicity formula for a local energy is derived for a supercritical parabolic equation with a source term containing a potential. The formula is then used to prove a partial regularity result for solutions which are on the boundary of the domain of attraction of zero.

MSC:

35D30 Weak solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
35K58 Semilinear parabolic equations
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