|
|||||
 |
|
|
|
|
Uniqueness of ground
states for pseudorelativistic Hartree equations
Enno Lenzmann |
|
Vol. 2 (2009), No. 1, 1–27
|
Abstract |
|
We prove uniqueness of ground states for the pseudorelativistic Hartree equation, in the regime of with sufficiently small -mass. This result shows that a uniqueness conjecture by Lieb and Yau [1987] holds true at least for except for at most countably many . Our proof combines variational arguments with a nonrelativistic limit, leading to a certain Hartree-type equation (also known as the Choquard–Pekard or Schrödinger–Newton equation). Uniqueness of ground states for this limiting Hartree equation is well-known. Here, as a key ingredient, we prove the so-called nondegeneracy of its linearization. This nondegeneracy result is also of independent interest, for it proves a key spectral assumption in a series of papers on effective solitary wave motion and classical limits for nonrelativistic Hartree equations. |
Keywords
pseudorelativistic Hartree equation, ground state,
uniqueness, boson stars
|
Mathematical Subject Classification 2000
Primary: 35Q55
|
Milestones
Received: 25 January 2008
Revised: 17 September 2008
Accepted: 11 January 2009
Published: 1 February 2009
|
Authors |
| Enno Lenzmann | |
| Massachusetts Institute of
Technology Department of Mathematics Room 2-230 Cambridge, MA 02139 United States |
|
|
