Displaying similar documents to “Nodal domains and spectral minimal partitions”

Numerical simulations for nodal domains and spectral minimal partitions

Virginie Bonnaillie-Noël, Bernard Helffer, Gregory Vial (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We recall here some theoretical results of Helffer [ (2007) doi:10.1016/j.anihpc.2007.07.004] about minimal partitions and propose numerical computations to check some of their published or unpublished conjectures and exhibit new ones.

Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue

Dimitri Mugnai (2005)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We give the precise behaviour of some solutions of a nonlinear elliptic B.V.P. in a bounded domain when a parameter approaches an eigenvalue of the principal part. If the nonlinearity has some regularity and the domain is for example convex, we also prove a nonlinear version of Courant’s Nodal theorem.