Partial Regularity for Harmonic Maps and Related Problems

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Global Solvability of the Cauchy Problem for the Landau-Lifshitz-Gilbert Equation in Higher Dimensions (2011, methodology): “In dimension n = 3, 4 perturbative methods based on elliptic problems on suitable time slices provide local regularity conditions for LLG in terms of certain scaling invariant space-time norms of Morrey-type, see [25, 24, 35].”
Partial regularity for biharmonic maps, revisited (2008, methodology): “To see (4) consider for simplicity the case of a biharmonic map u = (u 1 ,..., u n ) to a closed hypersurface N ⊂ R n with normal ν .A s in [ 9 ], the general case is obtained in similar”
Boundary regularity via Uhlenbeck–Rivière decomposition (2008, methodology): “In addition, the arguments used here and adapted from [RS08] to establish the Morrey type estimates for p < 2 seem to be more general in having generalizations to higher dimensional systems.”
Finite Time singularity of the Landau-Lifshitz-Gillbert Equation (2007, background): “[3, 4]), the above mentioned results by [10, 11, 16, 17] are limited to low dimensions.”
Conservation Laws for Fourth Order Systems in Four Dimensions (2006, background): “In Riviere and Struwe ( 2006 ), Struwe and the second author used the existence of an “almost” conservation law, which was motivated by the conservation law ( 1.”