Abstract
We make use of the flexibility of infinite-index solutions to the Allen–Cahn equation to show that, given any compact hypersurface of with , there is a bounded entire solution of the Allen–Cahn equation on whose zero level set has a connected component diffeomorphic (and arbitrarily close) to a rescaling of . More generally, we prove the existence of solutions with a finite number of compact connected components of prescribed topology in their zero level sets.
Citation
Alberto Enciso. Daniel Peralta-Salas. "Bounded solutions to the Allen–Cahn equation with level sets of any compact topology." Anal. PDE 9 (6) 1433 - 1446, 2016. https://doi.org/10.2140/apde.2016.9.1433
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