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Article Dans Une Revue Advances in Mathematics Année : 2014

A monotonicity formula and a Liouville-type theorem for a fourth order supercritical problem

Résumé

We consider Liouville-type and partial regularity results for the nonlinear fourth-order Lane-Emden equation. We give a complete classification of stable and finite Morse index solutions (whether positive or sign changing), in the full exponent range. We also compute an upper bound of the Hausdorff dimension of the singular set of extremal solutions. Our approach is motivated by Fleming's tangent cone analysis technique for minimal surfaces and Federer's dimension reduction principle in partial regularity theory. A key tool is the monotonicity formula for biharmonic equations.

Dates et versions

hal-00960908 , version 1 (19-03-2014)

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Louis Dupaigne, Juan Davila, Kelei Wang, Juncheng Wei. A monotonicity formula and a Liouville-type theorem for a fourth order supercritical problem. Advances in Mathematics, 2014, pp.10.1016/j.aim.2014.02.034. ⟨10.1016/j.aim.2014.02.034⟩. ⟨hal-00960908⟩
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