scholarly journals The regularity of solutions to some variational problems, including the p-Laplace equation for 2 ≤ p< 3

2017 ◽  
Vol 23 (4) ◽  
pp. 1543-1553 ◽  
Author(s):  
Arrigo Cellina
Keyword(s):  
Laplace Equation ◽  
Variational Problems ◽  
Regularity Of Solutions

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.

On the regularity of solutions to variational problems inBV(?)

1976 ◽  
Vol 149 (3) ◽  
pp. 281-286 ◽  
Author(s):  
Claus Gerhardt
Keyword(s):  
Variational Problems ◽  
Regularity Of Solutions

scholarly journals Regularity of solutions of the parabolic normalized p-Laplace equation

2018 ◽  
Vol 9 (1) ◽  
pp. 7-15 ◽  
Author(s):  
Fredrik Arbo Høeg ◽  
Peter Lindqvist
Keyword(s):  
Viscosity Solution ◽  
Laplace Equation ◽  
Time Derivative ◽  
Regularity Of Solutions

Abstract The parabolic normalized p-Laplace equation is studied. We prove that a viscosity solution has a time derivative in the sense of Sobolev belonging locally to {L^{2}} .

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