Existence and nonexistence in the liquid drop model

Nonexistence of Large Nuclei in the Liquid Drop Model

We give a simplified proof of the nonexistence of large nuclei in the liquid drop model and provide an explicit bound. Our bound is within a factor of 2.3 of the conjectured value and seems to be the first quantitative result. We consider the minimization problem E(A) = inf{E(Ω): |Ω| = A} over all measurable set Ω ⊂ R with the energy functional E [Ω] = PerΩ + 1 2 ∫∫

A Compactness Lemma and Its Application to the Existence of Minimizers for the Liquid Drop Model

The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an interesting problem in the calculus of variations: Find a set Ω ⊂ R3 with given volume A that minimizes the sum of its surface area and its Coulomb self energy. A ball minimizes the former and maximizes the latter, but the conjecture is that a ball is always a minimizer—when there is a minimizer. Even the exist...

Existence and Nonexistence of Solutionsfor

Harmonic Homeomorphisms: Existence and Nonexistence

These notes were prepared for International Workshop on Harmonic and Quasiconformal Mappings in Chennai, August 2010. They are based on several papers written jointly with Tadeusz Iwaniec, Jani Onninen, and Ngin-Tee Koh. The source papers are available from www.arxiv.org

Liquid-drop model of electron and atom

In the article is examined the liquid-drop model of electron and atom, which assumes existence of electron both in the form the ball-shaped formation and in the form liquid. This model is built on the same principles, on which was built the liquid-drop model of nucleus, proposed by Bohr and Weizsacker. The keywords: electron, the liquid-drop model of nucleus.