Non UBC
DSpace
Gabriele Mancini
2019-11-04T09:38:57Z
2019-05-07T14:39
I will discuss some results obtained in collaboration with Massimo
Grossi, Angela Pistoia and Daisuke Naimen concerning the existence of
nodal solutions for the problem
$$
-\Delta u = \lambda u e^{u^2+|u|^p} \text{ in }\Omega, u = 0 \text{ on
}\partial \Omega,
$$
where $\Omega\subseteq \mathbb R^2$ is a bounded smooth domain and
$p\to 1^+$.
If $\Omega$ is ball, it is known that the case $p=1$ defines a
critical threshold between the existence and the non-existence of
radially symmetric sign-changing solutions with $\lambda$ close to $0$.
In our work we construct a blowing-up family of nodal solutions to such
problem as $p\to 1^+$, when $\Omega$ is an arbitrary domain and
$\lambda$ is small enough. To our knowledge this is the first
construction of sign-changing solutions for a Moser-Trudinger type
critical equation on a non-symmetric domain.
https://circle.library.ubc.ca/rest/handle/2429/72177?expand=metadata
37.0 minutes
video/mp4
Author affiliation: Sapienza Università di Roma
Banff (Alta.)
10.14288/1.0384911
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Postdoctoral
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Partial differential equations
Differential geometry
Bubbling nodal solutions for a large perturbation of the Moser-Trudinger equation on planar domains.
Moving Image
http://hdl.handle.net/2429/72177