4 papers · 1 filter
Magnetic Neumann problems with Aharonov-Bohm potentials: boundary asymptotics of eigenvalues and splitting phenomena
Veronica Felli, Prasun Roychowdhury, Giovanni Siclari
We study a planar magnetic Schrödinger operator with an Aharonov-Bohm vector potential, under Neumann boundary conditions. Through a gauge transformation, the corresponding eigenva…
Miminization of the first eigenvalue of the Dirichlet Laplacian with a small volume obstacle
Benedetta Noris, Giovanni Siclari, Gianmaria Verzini
We consider the well-known shape optimization problem with spectral cost: minimizing the first eigenvalue of the Dirichlet Laplacian among all subdomains having prescribed volu…
Sobolev-type regularity and Pohozaev-type identities for some degenerate and singular problems
Veronica Felli, Giovanni Siclari
Sobolev-type regularity results are proved for solutions to a class of second order elliptic equations with a singular or degenerate weight, under non-homogeneous Neumann condition…
Unique continuation from a crack's tip under Neumann boundary conditions
Veronica Felli, Giovanni Siclari
We derive local asymptotics of solutions to second order elliptic equations at the edge of a -dimensional crack, with homogeneous Neumann boundary conditions prescribed on b…