New solutions for the lane-emden problem in planar domains

speaker: Isabella Ianni (Università degli Studi di Roma La Sapienza)

abstract: We consider the Lane-Emden problem

−∆u=
u
p−1u in Ω,

u=0 on ∂Ω,

where Ω ⊂ R2 is a smooth bounded domain. When the exponent p is large, the existence and multiplicity of solutions strongly depend on the geometric properties of the domain, which also deeply affect their qualitative behaviour. Remarkably, a wide variety of solutions, both positive and sign-changing, have been found when p is sufficiently large. In this talk, we focus on this topic and find new sign-changing solutions that exhibit an unexpected concentration phenomenon as p approaches +∞.

timetable:
Thu 12 Sep, 17:40 - 18:15, Aula Dini
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