scholarly journals On the Lavrentiev phenomenon for multiple integral scalar variational problems

2014 ◽  
Vol 266 (9) ◽  
pp. 5921-5954 ◽  
Author(s):  
Pierre Bousquet ◽  
Carlo Mariconda ◽  
Giulia Treu
Keyword(s):  
Multiple Integral ◽  
Variational Problems ◽  
Lavrentiev Phenomenon

Element removal method for singular minimizers in variational problems involving Lavrentiev phenomenon

1992 ◽  
Vol 439 (1905) ◽  
pp. 131-137 ◽  
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
Numerical Experiments ◽  
Variational Problems ◽  
Lavrentiev Phenomenon ◽  
Removal Method ◽  
Element Removal Method ◽  
Element Removal ◽  
Singular Minimizers

A numerical method called element removal method is designed to calculate singular minimizers which cannot be approximated by simple applications of standard numerical methods because of the so-called Lavrentiev phenomenon. The convergence of the method is proved. The results of numerical experiments show that the method is effective.

scholarly journals A TRUNCATION METHOD FOR DETECTING SINGULAR MINIMIZERS INVOLVING THE LAVRENTIEV PHENOMENON

2006 ◽  
Vol 16 (06) ◽  
pp. 847-867 ◽  
Author(s):  
YU BAI ◽  
ZHI-PING LI
Keyword(s):  
Numerical Method ◽  
Variational Problems ◽  
Numerical Results ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Minimizing Sequences ◽  
Lavrentiev Phenomenon ◽  
Absolute Minimizers ◽  
Sobolev Exponent ◽  
Singular Minimizers

A numerical method using the truncation technique on the integrand is developed for computing singular minimizers or singular minimizing sequences in variational problems involving the Lavrentiev phenomenon. It is proved that the method can detect absolute minimizers with various singularities whether the Lavrentiev phenomenon is involved or not. It is also proved that, when the absolute infimum is not attainable, the method can produce minimizing sequences. Numerical results on Manià's example and a two-dimensional problem involving the Lavrentiev phenomenon with continuous Sobolev exponent dependence, are given to show the efficiency of the method.

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