On biharmonic maps and their generalizations.

Autor: Pawel Strzelecki
Předmět:
Zdroj: Calculus of Variations & Partial Differential Equations; Dec2003, Vol. 18 Issue 4, p401-432, 32p
Abstrakt: 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 Hölder 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. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
Externí odkaz: