Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Interpretation of Lavrentiev phenomenon by relaxation: the higher order case
HTML articles powered by AMS MathViewer

by Marino Belloni PDF
Trans. Amer. Math. Soc. 347 (1995), 2011-2023 Request permission

Abstract:

We consider integral functionals of the calculus of variations of the form \[ F(u) = \int \limits _0^1 {f(x,u,u’, \ldots ,{u^{(n)}})dx} \] defined for $u \in {W^{n,\infty }}(0,1)$, and we show that the relaxed functional $F$ with respect to the weak $W_{{\text {loc}}}^{n,1}(0,1)$ convergence can be written as \[ \overline F (u) = \int \limits _0^1 {f(x,u,u’, \ldots ,{u^{(n)}})dx + L(u),} \] where the additional term $L(u)$, the Lavrentiev Gap, is explicitly identified in terms of $F$.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 49J45, 49J05
  • Retrieve articles in all journals with MSC: 49J45, 49J05
Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 2011-2023
  • MSC: Primary 49J45; Secondary 49J05
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1290714-9
  • MathSciNet review: 1290714