Existence of $p$ harmonic multiple valued maps into a separable Hilbert space
The general existence of $p$-Dirichlet energy minimizing maps into $Q_Q(l_2)$ is obtained.
math.AP↗
arXiv subjects
Jordan Goblet
Publications and source records attributed to Jordan Goblet.
Regularity of Dirichlet nearly minimizing multiple-valued functions
In this paper, we extend the related notions of Dirichlet quasiminimizer, $ω-$minimizer and almost minimizer to the framework of multiple-valued functions in the sense of Almgren and prove Holder regularity results. We also give examples of those minimizers with various branch sets.
math.AP↗
Lipschitz extension of multiple Banach-valued functions in the sense of Almgren
A multiple-valued function $f:X\to {\bf Q}_Q(Y)$ is essentially a rule assigning $Q$ unordered and non necessarily distinct elements of $Y$ to each element of $X$. We study the Lipschitz extension problem in this context by using two general Lipschitz extension theorems recently proved by U. Lang and T. Schlichenmaier. We prove that the pair $(X,{\bf Q}_Q(Y))$ has the Lipschitz extension property if $Y$ is a Banach space and $X$ is a metric space with a finite Nagata dimension. We also show that ${\bf Q}_{Q}(Y)$ is an absolute Lipschitz retract if $Y$ is a finite algebraic dimensional Banach space.
math.MG↗