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Saddle-shaped solutions of bistable diffusion equations in all of R2m

Autor
Cabre, X.; Mourao, J.
Tipus d'activitat
Article en revista
Revista
Journal of the European Mathematical Society
Data de publicació
2009
Volum
11
Número
4
Pàgina inicial
819
Pàgina final
843
DOI
https://doi.org/10.4171/JEMS/168 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/9286 Obrir en finestra nova
URL
http://www.ems-ph.org/journals/show_issue.php?issn=1435-9855&vol=11&iss=4 Obrir en finestra nova
Resum
We study the existence and instability properties of saddle-shaped solutions of the semilinear elliptic equation 􀀀1u D f .u/ in the whole R2m, where f is of bistable type. It is known that in dimension 2m D 2 there exists a saddle-shaped solution. This is a solution which changes sign in R2 and vanishes only on fjx1j D jx2jg. It is also known that this solution is unstable. In this article we prove the existence of saddle-shaped solutions in every even dimension, as well as their instability ...
Citació
Cabré, X.; Mourao, J. Saddle-shaped solutions of bistable diffusion equations in all of R2m. "Journal of the European Mathematical Society", 2009, vol. 11, núm. 4, p. 819-843.
Paraules clau
Allen–Cahn equation, Morse index, Simons cone, conjecture of De Giorgi on 1D symmetry, instability, saddle-shaped solutions
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

Participants