Interior Harnack Estimates: The State-of-the-Art for Quasilinear Singular Parabolic Equations

被引：4
作者：
Duzgun, Fatma Gamze [1 ,2 ]
Fornaro, Simona [3 ]
Vespri, Vincenzo [4 ]
机构：
[1] Univ Florence, Dipartimento Ingn Informaz, Via Santa Marta 3, I-50139 Florence, Italy
[2] Hacettepe Univ, Dept Math, TR-06800 Ankara, Turkey
[3] Univ Pavia, Dipartimento Matemat Felice Casorati, I-27100 Pavia, Italy
[4] Univ Florence, Dipartimento Matemat & Informat Ulisse Dini, I-50134 Florence, Italy
来源：
MILAN JOURNAL OF MATHEMATICS | 2015年 / 83卷 / 02期
关键词：
Degenerate and Singular Parabolic Equations; Pointwise Estimates; Harnack estimates; Weak solutions; NONNEGATIVE SOLUTIONS; WEAK SOLUTIONS; DIFFERENTIAL-EQUATIONS; HOLDER CONTINUITY; LOCAL BEHAVIOR; DEGENERATE; INEQUALITIES; PROOF; THEOREM;
D O I：
10.1007/s00032-015-0240-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we give some historical information about elliptic and parabolic Harnack inequalities. Then we state the main results known for Harnack inequalities of solutions to quasilinear degenerate parabolic equations. Lastly we focus our attention on Harnack inequalities of solutions to quasilinear singular parabolic equations where the theory did important steps forward in the last few years but still there are some points to be fully understood.
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页码：371 / 395
页数：25
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