4 papers
Validity of the linear marginal stability principle for monotonic fronts of the extended Fisher-Kolmogorov equation
R. D. Benguria, M. C. Depassier
The extended Fisher Kolmogorov equation with arbitrary positive , satisfying , has monotonic traveling fronts for .…
Connection between the Lieb--Thirring conjecture for Schroedinger operators and an isoperimetric problem for ovals on the plane
Rafael D. Benguria, Michael Loss
To determine the sharp constants for the one dimensional Lieb--Thirring inequalities with exponent gamma in (1/2,3/2) is still an open problem. According to a conjecture by Lieb an…
Oscillating minimizers of a fourth order problem invariant under scaling
R. Benguria, I. Catto, J. Dolbeault +1
By variational methods, we prove the inequality: $$ \int_{\mathbb{R}} u''{}^2 dx-\int_{\mathbb{R}} u'' u^2 dx\geq I \int_{\mathbb{R}} u^4 dx\quad \forall u\in L^4({\mathbb{R}}) {su…
A simple proof of a theorem of Laptev and Weidl
Rafael Benguria, Michael Loss
A new and elementary proof of a recent result of Laptev and Weidl is given. It is a sharp Lieb-Thirring inequality for one dimensional Schroedinger operators with matrix valued pot…