A boundary monotonicity inequality for variationally biharmonic maps and applications to regularity theory (Q1630070)

In this paper, the author derives a boundary monotonicity formula for a class of biharmonic maps with Dirichlet boundary conditions. This completes a gap in \textit{K. E. Mazowiecka}'s dissertation [Singularities of harmonic and biharmonic maps into compact manifolds. Warsaw: University of Warsaw (PhD Thesis) (2017)] (cf. [\textit{K. Mazowiecka}, Calc. Var. Partial Differ. Equ. 57, No. 6, Paper No. 143, 26 p. (2018; Zbl 1400.58004)]), thus providing the ``last missing ingredient for the proof of the full boundary regularity of minimizing harmonic maps''. The paper is carefully written and its introduction contains a good description of the mathematical framework used. Sections 2 and 3 consist of detailed proof of the results.