Regularity of the nodal set of segregated critical configurations under a weak reflection law

Details Regularity of the nodal set of segregated critical configurations under a weak reflection law Regularity of the nodal set of segregated critical configurations under a weak reflection law

2010-02-22

arxiv.org/abs/1002.3822v1

Mathematics

Analysis of PDEs

35 pages

Scientific paper

We deal with a class of Lipschitz vector functions $U=(u_1,...,u_h)$ whose components are non negative, disjointly supported and verify an elliptic equation on each support. Under a weak formulation of a reflection law, related to the Poho\u{z}aev identity, we prove that the nodal set is a collection of $C^{1,\alpha}$ hyper-surfaces (for every $0<\alpha<1$), up to a residual set with small Hausdorff dimension. This result applies to the asymptotic limits of reaction-diffusion systems with strong competition interactions, to optimal partition problems involving eigenvalues, as well as to segregated standing waves for Bose-Einstein condensates in multiple hyperfine spin states.

Affiliated with

Also associated with

No associations

Rating

Regularity of the nodal set of segregated critical configurations under a weak reflection law does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Regularity of the nodal set of segregated critical configurations under a weak reflection law, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regularity of the nodal set of segregated critical configurations under a weak reflection law will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-169002