80 research outputs found
Lp-gradient harmonic maps into spheres and SO(N)
We consider critical points of the energy , where maps locally into the sphere or ,
and is the formal fractional
gradient, i.e. is a composition of the fractional laplacian
with the -th Riesz transform. We show that critical points of this
energy are H\"older continuous.
As a special case, for , we obtain a new, more stable proof of Fuchs
and Strzelecki's regularity result of -harmonic maps into the sphere, which
is interesting on its own
A Note on Regularity for the n-dimensional H-System assuming logarithmic higher Integrability
We prove Holder continuity for solutions to the n-dimensional H-System
assuming logarithmic higher integrability of the solution
Interior and Boundary-Regularity for Fractional Harmonic Maps on Domains
We prove continuity on domains up to the boundary for n/2-polyharmonic maps
into manifolds. Technically, we show how to adapt Helein's direct approach to
the fractional setting. This extends a remark by the author that this is
possible in the setting of Riviere's famous regularity result for critical
points of conformally invariant variational functionals. Moreover, pointwise
behavior for the involved three-commutators is established. Continuity up to
the boundary is then obtained via an adaption of Hildebrandt and Kaul's
technique to the non-local setting
Nonlinear commutators for the fractional p-Laplacian and applications
We prove a nonlocal, nonlinear commutator estimate concerning the transfer of
derivatives onto testfunctions. For the fractional -Laplace operator it
implies that solutions to certain degenerate nonlocal equations are higher
differentiable. Also, weak fractional -harmonic functions which a priori are
less regular than variational solutions are in fact classical. As an
application we show that sequences of uniformly bounded -harmonic
maps converge strongly outside at most finitely many points
Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces
We construct a smooth compact n-dimensional manifold Y with one point
singularity such that all its Lipschitz homotopy groups are trivial, but
Lipschitz mappings Lip(S^n,Y) are not dense in the Sobolev space
W^{1,n}(S^n,Y). On the other hand we show that if a metric space Y is Lipschitz
(n-1)-connected, then Lipschitz mappings Lip(X,Y) are dense in N^{1,p}(X,Y)
whenever the Nagata dimension of X is bounded by n and the space X supports the
p-Poincare inequality
- …