Premium
Nonexistence of a Minimizer for Thomas–Fermi–Dirac–von Weizsäcker Model
Author(s) -
Lu Jianfeng,
Otto Felix
Publication year - 2014
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21477
Subject(s) - citation , dirac (video compression format) , mathematics , physics , computer science , combinatorics , library science , particle physics , neutrino
Ω×Ω 1 |x− y| dx dy. A nonexistence result similar to Theorem 1 also holds. Theorem 2. There exists constant V0 > 0, such that the variational problem (4) inf |Ω|=V E(Ω) does not have a minimizer if V ≥ V0. If the Coulomb term is not present in (1) and (3), a standard Modica-Mortela type result establishes a link between the two functional through Gamma convergence when the volume constraint m is large. This is no longer valid for the energy functionals (1) and (3) due to the Coulomb term. The connection between the two functionals is just on the formal level.