English

Resonances and Eigenvalues for the Constant Mean Curvature Equation

Analysis of PDEs 2022-10-11 v1

Abstract

In this paper we study resonances and eigenvalues for the nonlinear constant mean curvature eqn. linearized around the bubbles found by Brezis-Coron. This nonlinear eqn. is also called a H-system eqn. For degree one bubbles(the degree relates to a certain winding number) we only find resonances. For higher degree we prove eigenvalues do occur. Our goal is to eventually obtain dispersive estimates for the wave eqn. associated to the H-systems eqn. in its linear and non-linear form, a study of which was initiated by Chanillo-Yung.

Cite

@article{arxiv.2210.04580,
  title  = {Resonances and Eigenvalues for the Constant Mean Curvature Equation},
  author = {Sagun Chanillo},
  journal= {arXiv preprint arXiv:2210.04580},
  year   = {2022}
}
R2 v1 2026-06-28T03:08:17.499Z