On a constrained variational problem with an arbitrary number of free boundaries | Zendy

Paolo Tilli | Zendy

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On a constrained variational problem with an arbitrary number of free boundaries

Author(s) -

Paolo Tilli

Publication year - 2000

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/18

Subject(s) - lebesgue measure , mathematics , measure (data warehouse) , class (philosophy) , connection (principal bundle) , lebesgue integration , space (punctuation) , dirichlet distribution , set (abstract data type) , dirichlet problem , pure mathematics , mathematical analysis , combinatorics , computer science , boundary value problem , geometry , database , artificial intelligence , programming language , operating system

We study the problem of minimizing the Dirichlet integral among all functions u ∈ H 1 (Ω) whose level sets {u = li } have prescribed Lebesgue measure αi . This problem was introduced in connection with a model for the interface between immiscible fluids. The existence of minimizers is proved with an arbitrary number of level-set constraints, and their regularity is investigated. Our technique consists in enlarging the class of admissible functions to the whole space H 1 (Ω), penalizing those functions whose level sets have measures far from those required; in fact, we study the minimizers of

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