Double layered solutions to the extended Fisher–Kolmogorov P.D.E.

We construct double layered solutions to the extended Fisher–Kolmogorov P.D.E., under the assumption that the set of minimal heteroclinics of the corresponding O.D.E. satisfies a separation condition. The aim of our work is to provide for the extended Fisher–Kolmogorov equation, the first examples of two-dimensional minimal solutions, since these solutions play a crucial role in phase transition models, and are closely related to the De Giorgi conjecture.BERC 2018-2021 program, BCAM Severo Ochoa accreditation SEV-2017-0718, MTM2017-82184- R, National Science Centre, Poland (Grant No. 2017/26/E/ST1/00817)