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Andrea Malchiodi

Compactness of solutions to some geometric fourth-order equations

We prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant Q-curvature. As a byproduct of our method, we also obtain compactness of such metrics.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2006, 05/2006
Pages: 137 - 174

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