*PDEs: Italia vs España*
Jueves 28 de enero, 15 - 17 horas.
*Benedetta Noris (Politecnico di Milano).*
*Título: *Symmetric solutions to supercritical elliptic problems.
*Abstract:* When searching for solutions to Sobolev-supercritical elliptic
problems, a major difficulty is the lack of Sobolev embeddings, that
entrains a lack of compactness. In this talk, I will discuss how symmetry
and monotonicity properties can help to overcome this obstacle. In
particular, I will present a recent result concerning the existence of
axially symmetric solutions to a semilinear equation, in collaboration with
A. Boscaggin, F. Colasuonno and T. Weth.
*Antonio J. Fernández (University of Bath).*
*Título:* The nonlinear Schrödinger equation in the half-space.
*Abstract:* We consider the (stationary) nonlinear Schrödinger equation in
the half-space with non-homogeneous constant Dirichlet boundary conditions.
We analyse the existence, non-existence, and multiplicity of smooth bounded
positive solutions. We show that the existence and multiplicity depend in a
striking way on the boundary value and also on the dimension. The talk is
based on a joint work with Tobias Weth.