scholarly journals Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions

1989 ◽  
Vol 105 (3) ◽  
pp. 267-284 ◽  
Author(s):  
Paolo Marcellini
Keyword(s):  
Calculus Of Variations ◽  
Growth Conditions ◽  
Regularity Of Minimizers

Regularity of minimizers under limit growth conditions

2017 ◽  
Vol 153 ◽  
pp. 294-310 ◽  
Author(s):  
Giovanni Cupini ◽  
Paolo Marcellini ◽  
Elvira Mascolo
Keyword(s):  
Growth Conditions ◽  
Regularity Of Minimizers

Partial regularity of strong local minimizers of quasiconvex integrals with (p, q)-growth

2009 ◽  
Vol 139 (3) ◽  
pp. 595-621 ◽  
Author(s):  
Sabine Schemm ◽  
Thomas Schmidt
Keyword(s):  
Calculus Of Variations ◽  
Partial Regularity ◽  
Growth Conditions ◽  
Local Minimizers ◽  
Image Position

We consider strictly quasiconvex integralsin the multi-dimensional calculus of variations. For the C2-integrand f : ℝNn → ℝ we impose (p, q)-growth conditionswith γ, Γ > 0 and 1 < p ≤ q < min {p + 1/n, p(2n − 1)/(2n − 2)}. Under these assumptions we prove partial C1, αloc-regularity for strong local minimizers of F and the associated relaxed functional F.

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