Equilibrium shapes of charged droplets and related problems: (mostly) a review

• Autorzy: Michael Goldman , Berardo Ruffini
• Języki publikacji: EN

Abstrakty

EN

We review some recent results on the equilibrium shapes of charged liquid drops. We show that the natural variational model is ill-posed and how this can be overcome by either restricting the class of competitors or by adding penalizations in the functional. The original contribution of this note is twofold. First, we prove existence of an optimal distribution of charge for a conducting drop subject to an external electric field. Second, we prove that there exists no optimal conducting drop in this setting.

Słowa kluczowe

EN

Isoperimetry; non-local energies; charged drops

Kategorie tematyczne

• 49J45: Methods involving semicontinuity and convergence; relaxation
• 49S05: Variational principles of physics (should also be assigned at least one other classification number in section 49)
• 49J40: Variational methods including variational inequalities

• Wydawca: De Gruyter Open
• Czasopismo: Geometric Flows
• Rocznik: 2017
• Tom: 2
• Numer: 1

Daty

wydano

2017-12-20

otrzymano

2017-09-15

zaakceptowano

2017-10-26

online

2017-12-29

Twórcy

autor

Michael Goldman

• ,,

autor

Berardo Ruffini

• 5,,

Identyfikatory

DOI

10.1515/geofl-2017-0004