Estimates for the lowest eigenvalue of magnetic Laplacians

TY - JOUR

T1 - Estimates for the lowest eigenvalue of magnetic Laplacians

AU - Ekholm, Tomas

AU - Kovařík, Hynek

AU - Portmann, Fabian Daniel

PY - 2016/7/1

Y1 - 2016/7/1

N2 - We prove various estimates for the first eigenvalue of the magnetic Dirichlet Laplacian on a bounded, open, simply connected domain in two dimensions. When the magnetic field is constant, we give lower and upper bounds in terms of geometric quantities of the domain. We furthermore prove a lower bound for the first magnetic Neumann eigenvalue in the case of constant magnetic field.

AB - We prove various estimates for the first eigenvalue of the magnetic Dirichlet Laplacian on a bounded, open, simply connected domain in two dimensions. When the magnetic field is constant, we give lower and upper bounds in terms of geometric quantities of the domain. We furthermore prove a lower bound for the first magnetic Neumann eigenvalue in the case of constant magnetic field.

U2 - 10.1016/j.jmaa.2016.02.073

DO - 10.1016/j.jmaa.2016.02.073

M3 - Journal article

SN - 0022-247X

VL - 439

SP - 330

EP - 346

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -