Geodesic
Epsilon-regularity for almost-minimizers of anisotropic free interface problem with Hölder dependence on the position
Luca Esposito1 orcid ; Lorenzo Lamberti1 orcid ; Giovanni Pisante2 orcid
1Università degli Studi di Salerno, Fisciano, Italy
2Università della Campania Luigi Vanvitelli, Caserta, Italy
Interfaces and free boundaries, Tome 27 (2025) no. 4, pp. 619-658

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DOI

We establish an ε-regularity result for almost-minimizers of a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type. The surface energy exhibits anisotropic behavior and is defined by means of an ellipsoidal density that is Hölder continuous with respect to the position variable.
DOI : 10.4171/ifb/535
Classification : 49Q10, 49N60, 49Q20
Mots-clés : anisotropic surface energies, free boundary problem, epsilon-regularity, volume constraint

Luca Esposito  1   ; Lorenzo Lamberti  1   ; Giovanni Pisante  2

1 Università degli Studi di Salerno, Fisciano, Italy
2 Università della Campania Luigi Vanvitelli, Caserta, Italy 
Luca Esposito; Lorenzo Lamberti; Giovanni Pisante. Epsilon-regularity for almost-minimizers of anisotropic free interface problem with Hölder dependence on the position. Interfaces and free boundaries, Tome 27 (2025) no. 4, pp. 619-658. doi: 10.4171/ifb/535
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     author = {Luca Esposito and Lorenzo Lamberti and Giovanni Pisante},
     title = {Epsilon-regularity for almost-minimizers of anisotropic free interface problem with {H\"older} dependence on the position},
     journal = {Interfaces and free boundaries},
     pages = {619--658},
     year = {2025},
     volume = {27},
     number = {4},
     doi = {10.4171/ifb/535},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/535/}
}
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