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

[1] Monotonicity and one-dimensional symmetry for solutions of -Δpu = f(u) in half-spaces
Farina, Alberto
Montoro, Luigi
Sciunzi, Berardino
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2012, 43 (1-2) : 123 - 145
[2] Monotonicity and one-dimensional symmetry for solutions of −Δpu = f(u) in half-spaces
Alberto Farina
Luigi Montoro
Berardino Sciunzi
Calculus of Variations and Partial Differential Equations, 2012, 43 : 123 - 145
[3] A NOTE ON THE MONOTONICITY OF SOLUTIONS FOR FRACTIONAL EQUATIONS IN HALF-SPACES
Barrios, B.
Garcia-Melian, J.
Quaas, A.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 147 (07) : 3011 - 3019
[4] Monotonicity results in half-spaces for the p-Laplacian
Sciunzi, Berardino
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2015, 145 (03) : 597 - 610
[5] MONOTONICITY AND SYMMETRY OF POSITIVE SOLUTIONS TO DEGENERATE QUASILINEAR ELLIPTIC SYSTEMS IN HALF-SPACES AND STRIPS
Phuong Le
Hoang-Hung Vo
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2022, 21 (03) : 1027 - 1048
[6] Monotonicity of solutions of quasilinear degenerate elliptic equation in half-spaces
Alberto Farina
Luigi Montoro
Berardino Sciunzi
Mathematische Annalen, 2013, 357 : 855 - 893
[7] Monotonicity of solutions of quasilinear degenerate elliptic equation in half-spaces
Farina, Alberto
Montoro, Luigi
Sciunzi, Berardino
MATHEMATISCHE ANNALEN, 2013, 357 (03) : 855 - 893
[8] Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
Barrios, B.
Del Pezzo, L.
Garcia-Melian, J.
Quaas, A.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2017, 56 (02)
[9] Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
B. Barrios
L. Del Pezzo
J. García-Melián
A. Quaas
Calculus of Variations and Partial Differential Equations, 2017, 56
[10] Monotonicity of solutions to degenerate p-Laplace problems with a gradient term in half-spaces
Le, Phuong
Huynh, Nhat Vy
ANALYSIS AND MATHEMATICAL PHYSICS, 2024, 14 (03)

← 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