Boundary estimates for certain degenerate and singular parabolic equations

被引：10
|
作者：
Avelin, Benny [1 ]
Gianazza, Ugo [2 ]
Salsa, Sandro [3 ]
机构：
[1] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden
[2] Univ Pavia, Dipartimento Matemat F Casorati, Via Ferrata 1, I-27100 Pavia, Italy
[3] Politecn Milan, Dipartimento Matemat F Brioschi, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy
来源：
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2016年 / 18卷 / 02期
关键词：
Degenerate and singular parabolic equations; Harnack estimates; boundary Harnack inequality; Carleson estimate; LIPSCHITZ FREE-BOUNDARIES; P-HARMONIC-FUNCTIONS; NONNEGATIVE SOLUTIONS; HARNACK INEQUALITY; 2-PHASE PROBLEMS; ELLIPTIC-OPERATORS; REGULARITY; BEHAVIOR; PRINCIPLE; LAPLACIAN;
D O I：
10.4171/JEMS/593
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic p-Laplace equation. Assuming that such solutions continuously vanish on some distinguished part of the lateral part S-T of a Lipschitz cylinder, we prove Carleson-type estimates, and deduce some consequences under additional assumptions on the equation or the domain. We then prove analogous estimates for non-negative solutions to a class of degenerate/singular parabolic equations of porous medium type.
引用
收藏
页码：381 / 424
页数：44
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