590 research outputs found
Gradient estimates and blow-up analysis for stationary harmonic maps
For stationary harmonic maps between Riemannian manifolds, we provide a
necessary and sufficient condition for the uniform interior and boundary
gradient estimates in terms of the total energy of maps. We also show that if
analytic target manifolds do not carry any harmonic S^2, then the singular sets
of stationary maps are m \leq n - 4 rectifiable. Both of these results follow
from a general analysis on the defect measures and energy concentration sets
associated with a weakly converging sequence of stationary harmonic maps.Comment: 45 pages, published versio
Range descriptions for the spherical mean Radon transform
The transform considered in the paper averages a function supported in a ball
in \RR^n over all spheres centered at the boundary of the ball. This Radon
type transform arises in several contemporary applications, e.g. in
thermoacoustic tomography and sonar and radar imaging. Range descriptions for
such transforms are important in all these areas, for instance when dealing
with incomplete data, error correction, and other issues. Four different types
of complete range descriptions are provided, some of which also suggest
inversion procedures. Necessity of three of these (appropriately formulated)
conditions holds also in general domains, while the complete discussion of the
case of general domains would require another publication.Comment: LATEX file, 55 pages, two EPS figure
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