@article{5c85d5b3b0524e068c44476c44409706,

title = "Regularity of minimizers of shape optimization problems involving perimeter",

abstract = "We prove the existence and regularity of optimal shapes for the problem min{P(Ω)+G(Ω):Ω⊂D,|Ω|=m}, where P denotes the perimeter, |⋅| is the volume, and the functional G is either one of the following: • the Dirichlet energy Ef, with respect to a (possibly sign-changing) function f∈Lp;• a spectral functional of the form F(λ1,…,λk), where λk is the kth eigenvalue of the Dirichlet Laplacian and F:Rk→R is locally Lipschitz continuous and increasing in each variable.The domain D is the whole space Rd or a bounded domain. We also give general assumptions on the functional G so that the result remains valid.",

keywords = "Dirichlet energy, Regularity, Shape optimization, Spectral functional",

author = "{De Philippis}, Guido and Jimmy Lamboley and Michel Pierre and Bozhidar Velichkov",

note = "Funding Information: This work was supported by the projects ANR-12-BS01-0007 OPTIFORM financed by the French Agence Nationale de la Recherche (ANR). G.D.P. is supported by the MIUR SIR-grant “Geometric Variational Problems” ( RBSI14RVEZ ). G.D.P. is a member of the “Gruppo Nazionale per l'Analisi Matematica, la Probabilit{\'a} e le loro Applicazioni” (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). Funding Information: This work was supported by the projects ANR-12-BS01-0007 OPTIFORM financed by the French Agence Nationale de la Recherche (ANR). G.D.P. is supported by the MIUR SIR-grant ?Geometric Variational Problems? (RBSI14RVEZ). G.D.P. is a member of the ?Gruppo Nazionale per l'Analisi Matematica, la Probabilit? e le loro Applicazioni? (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). Publisher Copyright: {\textcopyright} 2017 Elsevier Masson SAS",

year = "2018",

month = jan,

doi = "10.1016/j.matpur.2017.05.021",

language = "English (US)",

volume = "109",

pages = "147--181",

journal = "Journal des Mathematiques Pures et Appliquees",

issn = "0021-7824",

publisher = "Elsevier Masson SAS",

}