The "hot spots" conjecture on the Vicsek set

Abstract

We prove the “hot spots” conjecture on the Vicsek set. Specifically, we will show that every eigenfunction of the second smallest eigenvalue of the Neumann Laplacian on the Vicsek set attains its maximum and minimum on the boundary.

Keywords

• analysis on fractals
• hot spots conjecture
• vicsek set
• 28a80
• 47a75