Monotonicity in half-spaces of positive solutions to -Δpu = f(u) in the case p > 2

被引：0

作者：

Farina, Alberto ^{[1
]}

Montoro, Luigi ^{[2
]}

Sciunzi, Berardino ^{[2
]}

机构：

[1] Univ Picardie Jules Verne, CNRS, LAMFA, UMR 7352, Amiens, France

[2] Univ Calabria, Dipartimento Matemat & Informat, Ponte Pietro Bucci 31B, I-87036 Cosenza, Italy

来源：

ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE | 2017年 / 17卷 / 04期

关键词：

ELLIPTIC-EQUATIONS; REGULARITY; SYMMETRY; MAXIMUM; CLASSIFICATION; INEQUALITIES; EXISTENCE; PRINCIPLE;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider weak distributional solutions to the equation -Delta(p)u f(u) in half-spaces under zero Dirichlet boundary condition. We assume that the nonlinearity is positive and superlinear at zero. For p > 2 (the case 1 < p <= 2 is already known) we prove that any positive solution is strictly monotone increasing in the direction orthogonal to the boundary of the half-space. As a consequence we deduce some Liouville-type theorems for the Lane-Emden-equation. Furthermore any nonnegative solution turns out to be C-2,C- (alpha) smooth.

引用

页码：1207 / 1229

页数：23

共 47 条

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Monotonicity in half-spaces of positive solutions to -Δpu = f(u) in the case p &gt; 2

Monotonicity in half-spaces of positive solutions to -Δpu = f(u) in the case p > 2