Mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with non-smooth coefficients

被引:0
|
作者
Malagoli, Emanuele [1 ]
Pallara, Diego [2 ,3 ,4 ,5 ]
Polidoro, Sergio [1 ]
机构
[1] Univ Modena & Reggio Emilia, Dipartimento Sci Fis Informat & Matemat, Modena, Italy
[2] Univ Salento, Dipartimento Matemat & Fis Ennio De Giorgi, Lecce, Italy
[3] INFN, Sez Lecce, Lecce, Italy
[4] Univ Salento, Dipartimento Dimatemat & Fis Ennio De Giorgi, Ex Collegio Fiorini Via Arnesano, Lecce, Italy
[5] INFN, Sez Lecce, Ex Collegio Fiorini Via Arnesano, Lecce, Italy
关键词
mean value formulas; uniformly parabolic operators; BEHAVIOR;
D O I
10.1002/mana.202100612
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with low regularity of the coefficients. We then use them to prove the parabolic strong maximum principle and the parabolic Harnack inequality. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C-1-boundary, the other stated for sets with finite perimeter.
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页码:4236 / 4263
页数:28
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