On Lipschitz regularity of minimizers of a calculus of variations problem with non locally bounded Lagrangians

2006 ◽  
Vol 343 (1) ◽  
pp. 69-74 ◽  
Author(s):  
Marc Quincampoix ◽  
Nadia Zlateva
Keyword(s):  
Calculus Of Variations ◽  
Lipschitz Regularity ◽  
Regularity Of Minimizers

Linearisation at infinity and Lipschitz estimates for certain problems in the calculus of variations

1986 ◽  
Vol 102 (3-4) ◽  
pp. 291-303 ◽  
Author(s):  
Michel Chipot ◽  
Lawrence C. Evans
Keyword(s):  
Optimal Design ◽  
Calculus Of Variations ◽  
Design Problem ◽  
Blow Up ◽  
Optimal Design Problem ◽  
Lagrange Equations ◽  
Lipschitz Regularity ◽  
Locally Lipschitz ◽  
Lipschitz Estimates

SynopsisWe demonstrate local Lipschitz regularity for minimisers of certain functionals which are appropriately convex and quadratic near infinity. The proof employs a blow-up argument entailing a linearisation of the Euler—Lagrange equations “at infinity”. As a application, we prove that minimisers for the relaxed optimal design problem derived by Kohn and Strang [3] are locally Lipschitz.

A Lipschitz regularity theorem

2007 ◽  
Vol 27 (6) ◽  
pp. 1713-1718 ◽  
Author(s):  
FRANCIS CLARKE
Keyword(s):  
Calculus Of Variations ◽  
Elementary Proof ◽  
Basic Problem ◽  
Regularity Theorem ◽  
Lipschitz Regularity

AbstractThis paper gives a direct and elementary proof of the fact that under hypotheses of Tonelli type, solutions to the basic problem in the calculus of variations are Lipschitz when the Lagrangian is autonomous. This fact was first proved by Clarke and Vinter in 1985, using other methods.

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