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; email@example.com.
2 Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal; firstname.lastname@example.org.
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
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