We establish both local and global well-posedness of the heat flow of polyharmonic maps from R to a compact Riemannian manifold without boundary for initial data with small BMO norms.

It has been suggested that transient osteoporosis or the bone marrow oedema syndrome (BMOS) may be the initial phase of osteonecrosis of the femoral head (ONFH) and that there may be a common pathophysiology. In this study, we have assessed the MR images of 200 consecutive patients with ONFH in respect of the BMO pattern in order to test this hypothesis. This pattern was not observed in the ear...

For 2 (?1; 1), let Q (R n) be the space of all measurable functions with supp`(I)] 2?n Z I Z I jf(x) ? f(y)j 2 jx ? yj n+2 dx dy < 1; where the supremum is taken over all cubes I with the edge length`(I) and the edges parellel to the coordinate axes in R n. If 2 (?1; 0), then Q (R n) = BMO(R n), and if 2 1; 1), then Q (R n) = fconstantsg. In the present paper, we discuss the case 2 0; 1). These...