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

[11] Monotonicity of positive solutions to quasilinear elliptic equations in half-spaces with a changing-sign nonlinearity
Francesco Esposito
Alberto Farina
Luigi Montoro
Berardino Sciunzi
Calculus of Variations and Partial Differential Equations, 2022, 61
[12] Monotonicity of positive solutions to quasilinear elliptic equations in half-spaces with a changing-sign nonlinearity
Esposito, Francesco
Farina, Alberto
Montoro, Luigi
Sciunzi, Berardino
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2022, 61 (04)
[13] Monotonicity in Half-spaces for p-Laplace Problems with a Sublinear Nonlinearity
Le, Phuong
POTENTIAL ANALYSIS, 2024,
[14] ON MONOTONICITY OF SOLUTIONS OF DIRICHLET PROBLEM FOR SOME QUASILINEAR ELLIPTIC EQUATIONS IN HALF-SPACES
Salieva, O. A.
EURASIAN MATHEMATICAL JOURNAL, 2015, 6 (04): : 59 - 76
[15] Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces
Farina, Alberto
Montoro, Luigi
Riey, Giuseppe
Sciunzi, Berardino
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2015, 32 (01): : 1 - 22
[16] Monotonicity and Symmetry of Nonnegative Solutions to -Δu = f(u) in Half-Planes and Strips
Farina, Alberto
Sciunzi, Berardino
ADVANCED NONLINEAR STUDIES, 2017, 17 (02) : 297 - 310
[17] RIGOROUS SOLUTIONS OF MILNES PROBLEM FOR 2 ADJACENT HALF-SPACES
KORN, A
NUKLEONIK, 1967, 9 (05): : 237 - &
[18] On positive solutions of the equation ΔU plus f(|x|)Up=0 in Rn, n > 2
Tadie
PARTIAL DIFFERENTIAL EQUATIONS: THEORY AND NUMERICAL SOLUTION, 2000, 406 : 322 - 328
[19] THE HEAD WAVE AT THE BOUNDARY OF 2 HEREDITARY-ELASTIC HALF-SPACES - THE CASE OF A LINEAR SOURCE
LOKSHIN, AA
PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS, 1994, 58 (01): : 171 - 176
[20] RESPONSE OF A DIRECTIONAL ARRAY TO A FIELD OF REFRACTED WAVES IN THE CASE OF AN INTERFACE BETWEEN 2 HOMOGENEOUS HALF-SPACES
GERASIMENKO, SA
SHARFARETS, BP
SOVIET PHYSICS ACOUSTICS-USSR, 1990, 36 (06): : 551 - 552

← 1 2 3 4 5 →

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