4 citations · 8 across the 19 of their papers we have counts for
5 papers · 2 filters
Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups
Rupert L. Frank, Bernard Helffer, Ari Laptev
We show that the -th Dirichlet eigenvalue of the sub-Laplacian on an open set of a Carnot group is greater than the -st Neumann eigenvalue. This extends earlier results i…
On the magnetic Dirichlet to Neumann operator on the disk -- strong diamagnetism and strong magnetic field limit--
Helffer Bernard, Nicoleau François
Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operato…
The index of sub-laplacians: beyond contact manifolds
Magnus Goffeng, Bernard Helffer
In this paper we study the following question: do sub-Laplacian type operators have non-trivial index theory on Carnot manifolds in higher degree of nilpotency? The problem relates…
Global counterexamples to uniqueness for a Calderón problem with conductivities
Thierry Daudé, Bernard Helffer, Niky Kamran +1
Let , , be a fixed smooth bounded domain, and let be a smooth conductivity in . Consider a non-zero frequency which does not belong to…
Trace formulas for the magnetic Laplacian and Dirichlet to Neumann operator -- Explicit expansions --
Bernard Helffer, François Nicoleau
Inspired by a recent paper of G. Liu and X. Tan (2023), we would like to measure how the magnetic effect appears in the heat trace formula associated with the magnetic Laplacian an…