A quasi-monotonicity formula and partial regularity for borderline solutions to a parabolic equation
Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 6, p. 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 : https://doi.org/10.1016/j.anihpc.2010.07.001
Keywords: Quasi-monotonicity formula, Partial regularity, Borderline solutions, Semilinear parabolic equations, Potential
@article{AIHPC_2010__27_6_1333_0,
     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},
     publisher = {Elsevier},
     volume = {27},
     number = {6},
     year = {2010},
     pages = {1333-1360},
     doi = {10.1016/j.anihpc.2010.07.001},
     zbl = {1213.35177},
     mrnumber = {2738324},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2010__27_6_1333_0}
}
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, Volume 27 (2010) no. 6, pp. 1333-1360. doi : 10.1016/j.anihpc.2010.07.001. http://www.numdam.org/item/AIHPC_2010__27_6_1333_0/

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