NONEXISTENCE OF VARIATIONAL MINIMIZERS RELATED TO A QUASILINEAR SINGULAR PROBLEM IN METRIC MEASURE SPACES

被引：5

作者：

Garain, Prashanta ^{[1
]}

Kinnunen, Juha ^{[1
]}

机构：

[1] Aalto Univ, Dept Math, POB 11100, FI-00076 Espoo, Finland

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 08期

关键词：

Analysis on metric measure spaces; Newtonian space; variational integral; minimizer; energy estimate; nonexistence; SEMILINEAR ELLIPTIC-EQUATIONS; STABLE-SOLUTIONS; REGULARITY; THEOREMS;

D O I：

10.1090/proc/15417

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we consider a variational problem related to a quasi-linear singular problem and obtain a nonexistence result in a metric measure space with a doubling measure and a Poincare inequality. Our method is purely variational and to the best of our knowledge, this is the first work concerning singular problems in a general metric setting.

引用

页码：3407 / 3416

页数：10

共 30 条

[1]

Anders Bjorn, 2011, EMS TRACTS MATH, V17

[2] Stability and qualitative properties of radial solutions of the Lane-Emden-Fowler equation on Riemannian models [J].

Berchio, Elvise ;

Ferrero, Alberto ;

Grillo, Gabriele .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2014, 102 (01) :1-35

[3] Semilinear elliptic equations with singular nonlinearities [J].

Boccardo, Lucio ;

Orsina, Luigi .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 37 (3-4) :363-380

[4] Regularity of radial minimizers and extremal solutions of semilinear elliptic equations [J].

Cabre, Xavier ;

Capella, Antonio .

JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 238 (02) :709-733

[5] Stable solutions to semilinear elliptic equations are smooth up to dimension 9 [J].

Cabre, Xavier ;

Ros-Oton, Xavier ;

Figalli, Alessio ;

Serra, Joaquim .

ACTA MATHEMATICA, 2020, 224 (02) :187-252

[6] Regularity of Stable Solutions up to Dimension 7 in Domains of Double Revolution [J].

Cabre, Xavier ;

Ros-Oton, Xavier .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2013, 38 (01) :135-154

[7] Regularity of Minimizers of Semilinear Elliptic Problems Up to Dimension 4 [J].

Cabre, Xavier .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2010, 63 (10) :1362-1380

[8]

Cabre Xavier, 2020, ARXIV200601445

[9] Existence and uniqueness for p-Laplace equations involving singular nonlinearities [J].

Canino, Annamaria ;

Sciunzi, Berardino ;

Trombetta, Alessandro .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2016, 23 (02)

[10] LOW DIMENSIONAL INSTABILITY FOR SEMILINEAR AND QUASILINEAR PROBLEMS IN RN [J].

Castorina, Daniele ;

Esposito, Pierpaolo ;

Sciunzi, Berardino .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (06) :1779-1793

← 1 2 3 →