Add to ORKGWe construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with Neumann boundary conditions is simple and such that the corresponding eigenfunction attains its strict maximum at an interior point of that domain.Research partially supported by NSF grant DMS-9700721
Abstract. We consider the problem of minimising the kth eigen-value, k ≥ 2, of the (p-)Laplacian wit...
Abstract. We prove that the second eigenvalue of the Laplacian with Robin boundary conditions is min...
AbstractApproximation formulas for the eigenvalues of the Laplacian with Dirichlet boundary conditio...
We introduce a new variational principle for the study of eigenvalues and eigenfunctions of the Lapl...
We prove the “hot spots” conjecture on the Vicsek set. Specifically, we will show that every eigenfu...
Abstract. The “hot spots conjecture ” of Jeffrey Rauch says that the second Neumann eigenfunction fo...
Consider a convex planar domain with two axes of symmetry. We show that the maximum and minimum of a...
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the b...
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the b...
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the b...
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the b...
Hot-spots conjecture, posed by J. Rauch, states that the hottest point on an insulated plate with ar...
We show that equality in Courant's nodal domain theorem can only be reached for a finite number of e...
We show that equality in Courant's nodal domain theorem can only be reached for a finite number of e...
We consider Dirichlet eigenfunctions of membrane problems. A counterexample to Payne's nodal li...
Abstract. We consider the problem of minimising the kth eigen-value, k ≥ 2, of the (p-)Laplacian wit...
Abstract. We prove that the second eigenvalue of the Laplacian with Robin boundary conditions is min...
AbstractApproximation formulas for the eigenvalues of the Laplacian with Dirichlet boundary conditio...
We introduce a new variational principle for the study of eigenvalues and eigenfunctions of the Lapl...
We prove the “hot spots” conjecture on the Vicsek set. Specifically, we will show that every eigenfu...
Abstract. The “hot spots conjecture ” of Jeffrey Rauch says that the second Neumann eigenfunction fo...
Consider a convex planar domain with two axes of symmetry. We show that the maximum and minimum of a...
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the b...
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the b...
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the b...
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the b...
Hot-spots conjecture, posed by J. Rauch, states that the hottest point on an insulated plate with ar...
We show that equality in Courant's nodal domain theorem can only be reached for a finite number of e...
We show that equality in Courant's nodal domain theorem can only be reached for a finite number of e...
We consider Dirichlet eigenfunctions of membrane problems. A counterexample to Payne's nodal li...
Abstract. We consider the problem of minimising the kth eigen-value, k ≥ 2, of the (p-)Laplacian wit...
Abstract. We prove that the second eigenvalue of the Laplacian with Robin boundary conditions is min...
AbstractApproximation formulas for the eigenvalues of the Laplacian with Dirichlet boundary conditio...