Regularity for some scalar variational problems under general growth conditions

1996 ◽  
Vol 90 (1) ◽  
pp. 161-181 ◽  
Author(s):  
P. Marcellini
Keyword(s):  
Variational Problems ◽  
Growth Conditions ◽  
General Growth

scholarly journals Regularity under sharp anisotropic general growth conditions

2009 ◽  
Vol 11 (1) ◽  
pp. 67-86
Author(s):  
Giovanni Cupini ◽  
◽  
Paolo Marcellini ◽  
Elvira Mascolo
Keyword(s):  
Growth Conditions ◽  
General Growth

scholarly journals Lipschitz Bounds and Nonautonomous Integrals

2021 ◽  
Author(s):  
Cristiana De Filippis ◽  
Giuseppe Mingione
Keyword(s):  
Variational Problems ◽  
Growth Conditions ◽  
Regularity Criteria ◽  
Regularity Of Solutions ◽  
Optimal Regularity ◽  
Lipschitz Regularity ◽  
Elliptic Case ◽  
Different Types ◽  
Vector Valued

AbstractWe provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range from those with unbalanced polynomial growth conditions to those with fast, exponential type growth. The results obtained are sharp with respect to all the data considered and also yield new, optimal regularity criteria in the classical uniformly elliptic case. We give a classification of different types of nonuniform ellipticity, accordingly identifying suitable conditions to get regularity theorems.

Sign in / Sign up

Export Citation Format

Share Document