A quasi-monotonicity formula and partial regularity for borderline solutions to a parabolic equation
Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 6, pp. 1333-1360.

A quasi-monotonicity formula for the solution to a semilinear parabolic equation u t =Δu+V(x)|u| p-1 u, p>(N+2)/(N-2) in Ω×(0,T) with 0-Dirichlet boundary condition is obtained. As an application, it is shown that for some suitable global weak solution u and any compact set QΩ×(0,T) there exists a close subset Q ' Q such that u is continuous in Q ' and the (N-4 p-1)-dimensional parabolic Hausdorff measure (N-4 p-1) (QQ ' ) of QQ ' is finite.

DOI : 10.1016/j.anihpc.2010.07.001
Mots clés : Quasi-monotonicity formula, Partial regularity, Borderline solutions, Semilinear parabolic equations, Potential
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     author = {Zheng, Gao-Feng},
     title = {A quasi-monotonicity formula and partial regularity for borderline solutions to a parabolic equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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     publisher = {Elsevier},
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Zheng, Gao-Feng. A quasi-monotonicity formula and partial regularity for borderline solutions to a parabolic equation. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 6, pp. 1333-1360. doi : 10.1016/j.anihpc.2010.07.001. http://www.numdam.org/articles/10.1016/j.anihpc.2010.07.001/

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