Abstract.
We study the Cahn-Hilliard equation in a bounded smooth domain without any symmetry assumptions. We prove that for any fixed positive integer K there exist interior K–spike solutions whose peaks have maximal possible distance from the boundary and from one another. This implies that for any bounded and smooth domain there exist interior K–peak solutions. The central ingredient of our analysis is the novel derivation and exploitation of a reduction of the energy to finite dimensions (Lemma 5.5) with variables which are closely related to the location of the peaks. We do not assume nondegeneracy of the points of maximal distance to the boundary but can do with a global condition instead which in many cases is weaker.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received March 5, 1999 / Accepted June 11, 1999
Rights and permissions
About this article
Cite this article
Wei, J., Winter, M. Multi-interior-spike solutions for the Cahn-Hilliard equation with arbitrarily many peaks. Calc Var 10, 249–289 (2000). https://doi.org/10.1007/s005260050153
Issue Date:
DOI: https://doi.org/10.1007/s005260050153