The Lavrentieff phenomenon for quadratic functionals
Riccardo De Arcangelis · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1995
The paper provides an example of an integral functional in more than two dimensions, with a symmetric and positively defined quadratic integrandq, exhibiting the Lavrentieff phenomenon on a ballBand on a linear boundary datumu0, 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.