Flat solutions of some non-Lipschitz autonomous semilinear equations may be stable for N≥ 3

2016/11/11 by Jesús Ildefonso Díaz, Díaz, Jesús Ildefonso, Jesús Hernández +3 · 1 citation
Mathematics · #35J60 #35J96 #35R35 #53C45 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35J60 #msc:35J96 #msc:35R35 #msc:53C45

paper · pdf · doi:10.48550/arxiv.1611.03584

30 pages, 3 figures

arxiv created 2016/11/11 · arxiv updated 2016/11/14

Abstract

We prove that flat ground state solutions (i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equations with a strong absorption term given by a non-Lipschitz function are unstable for dimensions N=1,2 and they can be stable for N≥ 3 for suitable values of the involved exponents.

Cited by

• Electron beams: partially flat solutions of a nonlinear elliptic equation with a singular absorption term

Related

• On the exact multiplicity of stable ground states of non-Lipschitz semilinear elliptic equations for some classes of starshaped sets
• Energy estimate up to the boundary for stable solutions to semilinear elliptic problems
• Energy stability for a class of semilinear elliptic problems
• Regularity of stable solutions to reaction-diffusion elliptic equations
• The boundedness of stable solutions to semilinear elliptic equations with linear lower bound on nonlinearities