Multiple solutions for a nonconvex variational problem with double-well potentials

2018 ◽  
Vol 39 (5) ◽  
pp. 1663-1669
Author(s):  
Xiaojun Lu ◽  
Xiaofen Lv ◽  
Guanghui Wen
Keyword(s):  
Variational Problem ◽  
Multiple Solutions ◽  
Nonconvex Variational Problem

Analysis of a Nonconvex Problem Related to Signal Selective Smoothing

1997 ◽  
Vol 07 (03) ◽  
pp. 313-328 ◽  
Author(s):  
M. Chipot ◽  
R. March ◽  
M. Rosati ◽  
G. Vergara Caffarelli
Keyword(s):  
Variational Problem ◽  
Existence Result ◽  
Minimizing Sequences ◽  
Qualitative Properties ◽  
Nonconvex Problem ◽  
Nonconvex Variational Problem ◽  
Selective Smoothing

We study some properties of a nonconvex variational problem. We fail to attain the infimum of the functional that has to be minimized. Instead, minimizing sequences develop gradient oscillations which allow them to reduce the value of the functional. We show an existence result for a perturbed nonconvex version of the problem, and we study the qualitative properties of the corresponding minimizer. The pattern of the gradient oscillations for the original nonperturbed problem is analyzed numerically.

scholarly journals Geometry and numerical continuation of multiscale orbits in a nonconvex variational problem

2020 ◽  
Vol 13 (4) ◽  
pp. 1269-1290 ◽  
Author(s):  
Annalisa Iuorio ◽  
◽  
Christian Kuehn ◽  
Peter Szmolyan ◽  
Keyword(s):  
Variational Problem ◽  
Numerical Continuation ◽  
Nonconvex Variational Problem

A nonconvex variational problem related to change of phase

1990 ◽  
Vol 21 (1) ◽  
pp. 113-138 ◽  
Author(s):  
Patricia Bauman ◽  
Daniel Phillips
Keyword(s):  
Variational Problem ◽  
Nonconvex Variational Problem
Sign in / Sign up

Export Citation Format

Share Document