scholarly journals Regularity of radial stable solutions to semilinear elliptic equations for the fractional Laplacian

2018 ◽  
Vol 17 (6) ◽  
pp. 2547-2575
Author(s):  
Tomás Sanz-Perela ◽  
Keyword(s):  
Elliptic Equations ◽  
Fractional Laplacian ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Stable Solutions

Singular solutions of semilinear elliptic equations with fractional Laplacian in entire space

2016 ◽  
Vol 18 (01) ◽  
pp. 1550024 ◽  
Author(s):  
Zhuoran Du
Keyword(s):  
Elliptic Equations ◽  
Singular Solution ◽  
Fractional Laplacian ◽  
Semilinear Elliptic Equations ◽  
Singular Solutions ◽  
Entire Space ◽  
Semilinear Elliptic ◽  
Supercritical Exponent ◽  
Extension Result

We consider the existence of positive singular solutions of the problem [Formula: see text] where [Formula: see text] and [Formula: see text]. We obtain the existence of positive singular solutions [Formula: see text] of this problem in space dimensions [Formula: see text] for the case [Formula: see text] under the condition [Formula: see text]. By the well-known Caffarelli–Silvestre extension result, the trace of [Formula: see text] is a positive singular solution for the following equation with a supercritical exponent [Formula: see text] where [Formula: see text] denotes the fractional Laplacian.

scholarly journals Stable solutions to semilinear elliptic equations are smooth up to dimension $9$

2020 ◽  
Vol 224 (2) ◽  
pp. 187-252 ◽  
Author(s):  
Xavier Cabré ◽  
Alessio Figalli ◽  
Xavier Ros-Oton ◽  
Joaquim Serra
Keyword(s):  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Stable Solutions

scholarly journals Boundedness of Stable Solutions to Semilinear Elliptic Equations: A Survey

2017 ◽  
Vol 17 (2) ◽  
Author(s):  
Xavier Cabré
Keyword(s):  
Elliptic Equations ◽  
Elliptic Problems ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems ◽  
Stable Solutions

AbstractThis article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known

Sign in / Sign up

Export Citation Format

Share Document