Blow-up analysis shows biharmonic 4-spheres or 4-halfspheres are the only obstruction to strong boundary compactness for variationally biharmonic maps in dimensions m >= 5.
Luckhaus, Partial H¨ older continuity for minima of c ertain energies among maps into a Riemannian manifold
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Blow-up analysis and boundary regularity for variationally biharmonic maps
Blow-up analysis shows biharmonic 4-spheres or 4-halfspheres are the only obstruction to strong boundary compactness for variationally biharmonic maps in dimensions m >= 5.