The Du Bois-Reymond relation in the calculus of variations

1934 ◽  
Vol 109 (1) ◽  
pp. 746-755 ◽  
Author(s):  
E. J. McShane



1995 ◽  
Author(s):  
Louis Massiah
Keyword(s):  


1914 ◽  
Vol 1 (5) ◽  
pp. 229-231
Keyword(s):  


1993 ◽  
Vol 81 (12) ◽  
pp. 5-14 ◽  
Author(s):  
P. François ◽  
P. Morlier
Keyword(s):  


2016 ◽  
Vol 1 (2) ◽  
pp. 99-109
Author(s):  
Joe Lockard
Keyword(s):  


2013 ◽  
Vol 1 ◽  
pp. 200-231 ◽  
Author(s):  
Andrea C.G. Mennucci

Abstract In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.







Sign in / Sign up

Export Citation Format

Share Document