In this note we present some Pohozaev-type identities that have been recently established in a joint work with Paul Laurain and Tristan Rivière in the framework of half-harmonic maps defined either on the real line or on the unit circle with values into a closed n-dimensional manifold. Weak half-harmonic maps are defined as critical points of the so-called half Dirichlet energy.By using the invariance of the half Dirichlet energy with respect to the trace of the Möbius transformations we derive a countable family of relations involving the Fourier coefficients of weak half-harmonic maps. We also present a short overview of Pohozaev formulas in 2-D in connection with Noether's theorem.
@article{8963,
title = {Some Remarks on Pohozaev-Type Identities},
journal = {Bruno Pini Mathematical Analysis Seminar},
year = {2018},
doi = {10.6092/issn.2240-2829/8963},
language = {EN},
url = {http://dml.mathdoc.fr/item/8963}
}
Da Lio, Francesca. Some Remarks on Pohozaev-Type Identities. Bruno Pini Mathematical Analysis Seminar, (2018), . doi : 10.6092/issn.2240-2829/8963. http://gdmltest.u-ga.fr/item/8963/