English

Concentration analysis for elliptic critical equations with no boundary control: ground-state blow-up

Analysis of PDEs 2025-01-09 v2

Abstract

We perform the apriori analysis of solutions to critical nonlinear elliptic equations on manifolds with boundary. The solutions are of minimizing type. The originality is that we impose no condition on the boundary, which leads us to assume L2L^2-concentration. We also analyze the effect of a non-homogeneous nonlinearity that results in the fast convergence of the concentration point.

Keywords

Cite

@article{arxiv.2310.14994,
  title  = {Concentration analysis for elliptic critical equations with no boundary control: ground-state blow-up},
  author = {Hussein Mesmar and Frédéric Robert},
  journal= {arXiv preprint arXiv:2310.14994},
  year   = {2025}
}

Comments

Dedicated to Yihong Du on the occasion of his 60th birthday. To appear in DCDS