Volume 7, 2002
|Page(s)||223 - 237|
|Published online||15 September 2002|
On a Volume Constrained Variational Problem in SBV²(Ω): Part I
CMAF, Universidade de Lisboa,
Av. Prof. Gama
Pinto, 2, 1649-003 Lisboa, Portugal and
Departamento de Matemática, Faculdade de Ciências, Universidade de
Lisboa, 1749-016 Lisboa, Portugal; firstname.lastname@example.org.
2 Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal; email@example.com.
Revised: 12 January 2001
Revised: 27 July 2001
Revised: 18 September 2001
We consider the problem of minimizing the energy among all functions u ∈ SBV²(Ω) for which two level sets have prescribed Lebesgue measure . Subject to this volume constraint the existence of minimizers for E(.) is proved and the asymptotic behaviour of the solutions is investigated.
Mathematics Subject Classification: 49J45 / 35R35 / 76T05
Key words: Special functions of bounded variation / level sets / lower semicontinuity / Γ-limit.
© EDP Sciences, SMAI, 2002
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.