Τίτλος: On the existence of N-junctions for a symmetric nonnegative potential with N + 1 zeros.

Ομιλητής: Giorgio Fusco (L'Aquila, Italy)

Σύνδεσμος: meet.google.com/sru-gxoc-gzw

Ημερομηνία: Παρασκευή 25/6/2021

Ώρα: 15:15

Περίληψη: We consider a nonnegative potential W : 2 → R which is invariant under CN, the rotation group of the regular polygon with N sides.
We assume that {W = 0} = {0, a, ωa, . . . , ωN−1a}, ω = rotation of 2πN, for some a ∈ R2\ {0}.

We prove that, if a certain condition is satisfied, there exists a N-junction, that is a solution U : R2 → R2 of the vector Allen-Cahn equation that avoids 0 and connects a, ωa, . . . , ωN−1a at infinity.

The proof is variational and is based on sharp lower and upper bounds for the energy and on a new pointwise estimate for vector minimizers.