TITLE

# On biharmonic maps and their generalizations

AUTHOR(S)
Pawel Strzelecki
PUB. DATE
December 2003
SOURCE
Calculus of Variations & Partial Differential Equations;Dec2003, Vol. 18 Issue 4, p401
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We give a new proof of regularity of biharmonic maps from four-dimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hï¿½lder inequalities is used next to prove continuity of solutions and higher integrability of their second order derivatives. As a byproduct, we also prove that a weak limit of biharmonic maps into a sphere is again biharmonic. The proof of regularity can be adapted to biharmonic maps on the Heisenberg group, and to other functionals leading to fourth order elliptic equations with critical nonlinearities in lower order derivatives.
ACCESSION #
11575816

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