Generalizations of Pleijel's nodal domain
GFM seminar
	    
	      FCUL, C6, room 6.2.33
	    
	    
                        
                        
                            2017-04-04 14:00
                            2017-04-04 15:00
                            2017-04-04
                            14:00
                            ..
                            15:00
                        
            
	    
            
	    
        by Corentin Léna (Università degli Studi di Torino)
Courant's nodal domain theorem tells us that an eigenfunction associated with the \(k^{th}\) eigenvalue of the Laplacian has at most \(k\) nodal domains. A. Pleijel showed in 1956 that for a given planar domain, eigenfunctions satisfying a Dirichlet boundary condition reach equality only for a finite number of \(k\). We will study a generalization of this theorem to Robin-type boundary conditions, including the Neumann one, in any dimension. We will also consider the sharper results that can be obtained for particular domains.
 
             
             
             
                
                
             
                
             Symmetries in Quantum Physics 2017
            Symmetries in Quantum Physics 2017
        