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Regularity of a fourth order nonlinear PDE with critical exponent
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 121, Number 2, April 1999
- pp. 215-257
- 10.1353/ajm.1999.0011
- Article
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In this paper we demonstrate the regularity of minimizers for a variational problem, a special case of which arises in spectral theory and conformal geometry. The associated Euler-Lagrange equation is fourth order semilinear; the leading term is the bilaplacian, and lower order terms appear at critical powers.