Bubbling phenomena for fourth-order four-dimensional PDEs with exponential growth

Druet, O.; Robert, F.

doi:10.1090/S0002-9939-05-08330-9

Bubbling phenomena for fourth-order four-dimensional PDEs with exponential growth
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Proc. Amer. Math. Soc. 134 (2006), 897-908 Request permission

Abstract:

We are concerned in this paper with the bubbling phenomenon for nonlinear fourth-order four-dimensional PDE’s. The operators in the equations are perturbations of the bi-Laplacian. The nonlinearity is of exponential growth. Such equations arise naturally in statistical physics and geometry. As a consequence of our theorem we get a priori bounds for solutions of our equations.

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