Article contents
The Lavrentieff phenomenon for quadratic functionals
Published online by Cambridge University Press: 14 November 2011
Abstract
The paper provides an example of an integral functional in more than two dimensions, with a symmetric and positively defined quadratic integrand q, exhibiting the Lavrentieff phenomenon on a ball B and on a linear boundary datum u0, i.e. for which
The example is also utilised to discuss nonidentity between some relaxation procedures for a quadratic integral functional and to provide a weighted Sobolev space in the Hilbert case in which smooth functions are not dense.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 2 , 1995 , pp. 329 - 339
- Copyright
- Copyright © Royal Society of Edinburgh 1995
References
- 2
- Cited by