Luca Battaglia, Isabella Ianni, Angela Pistoia
Published 2024-07-22Version 1
We consider the Lane-Emden problem on planar domains. When the exponent is large, the existence and multiplicity of solutions strongly depend on the geometric properties of the domain, which also deeply affect their qualitative behavior. Remarkably, a wide variety of solutions, both positive and sign-changing, have been found when the exponent is sufficiently large. In this paper, we focus on this topic and fine new sign-changing solutions that exhibit an unexpected concentration phenomenon as the exponent approaches infinity.
Some geometric properties of nonparametric $μ$-surfaces in $\mathbb{R}^3$
The Euler Equations in Planar Domains with Corners
Geometric Properties of the 2-D Peskin Problem
![QR code for arXiv:2407.15742 [math.AP]](http://oss.arxitics.com/images/favicon.svg)