Eigenvalue estimates and critical temperature in zero fields for enhanced surface superconductivity

We derive estimates for the principal eigenvalue of the boundary value problem in Ω, on ∂Ω, with α > 0 and a bounded domain. In the context of superconductivity, our results show the increase of the critical temperature in zero fields for systems with enhanced surface superconductivity. In term of long time behavior of a Brownian motion with creation of particles at the boundary, our study gives estimates for the expected number of particles inside the domain. Tiziana Giorgi: Funding to this author was provided by the National Science Foundation-funded ADVANCE Institutional Transformation Program at NMSU, fund # NSF0123690