Non-transversal intersection of the free and fixed boundary in the mean-field theory of superconductivity

TL;DR

This paper proves that the free and fixed boundaries intersect non-transversally in certain obstacle problems related to superconductivity, providing a classification of blow-up solutions in two dimensions.

Contribution

It establishes non-transversal boundary intersection and classifies blow-up solutions for fully nonlinear elliptic obstacle problems in the context of superconducting vortices.

Findings

Non-transversal intersection of boundaries proven

Classification of blow-up solutions provided

Results specific to two-dimensional problems

Abstract

Non-transversal intersection of the free and fixed boundary is shown to hold and a classification of blow-up solutions is given for obstacle problems generated by fully nonlinear uniformly elliptic operators in two dimensions which appear in the mean-field theory of superconducting vortices.