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 Holder 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Calculus of Variations and Partial Differential Equations
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
