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Characteristic functions on the boundary of a planar domain need not be traces of least gradient functions
Mickael Dos Santos
Given a smooth bounded planar domain, we construct a compact set on the boundary s.t. its characteristic function is not the trace of a least gradient function. This generalize the…
Local Minimizers of the Ginzburg-Landau Functional with Prescribed Degrees
Mickaël Dos Santos
We consider, in a smooth bounded multiply connected domain $\dom\subset\R^2$, the Ginzburg-Landau energy $\d E_\v(u)=1/2\int_\dom{|\n u|^2}+\frac{1}{4\v^2}\int_\dom{(1-|u|^2)^2}$ s…
The Ginzburg-Landau functional with a discontinuous and rapidly oscillating pinning term. Part II: the non-zero degree case
Mickaël Dos Santos
We consider minimizers of a Ginzburg-Landau energy with a discontinuous and rapidly oscillating pinning term, subject to a Dirichlet boundary condition of degree . The pinni…
Study of a 3D Ginzburg-Landau functional with a discontinuous pinning term
Mickaël Dos Santos
In a convex domain , we consider the minimization of a 3D-Ginzburg-Landau type energy $E_\v(u)=1/2\int_Ø|\n u|^2+\frac{1}{2\v^2}(a^2-|u|^2)^2$ with a discontinuous pi…