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The Lavrentieff phenomenon for quadratic functionals

Published online by Cambridge University Press:  14 November 2011

Riccardo De Arcangelis
Riccardo De Arcangelis
Affiliation:
Dipartimento di Matematica ed Applicazioni ‘R. Caccioppoli’, Università degli Studi di Napoli ‘Federico II’, Complesso universitario ‘Monte S. Angelo‘, via Cintia, 80126 Napoli, Italy
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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

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