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Critical growth biharmonic elliptic problems under Steklov-type boundary conditions. (English) Zbl 1155.35018

The authors consider a fourth order nonlinear critical problem in a smooth bounded domain \(\Omega \subset\mathbb R^n\), \(n\geq 5\), with suitable boundary conditions. The interest in the problem arises from conformal geometry. Existence of a solution for such a kind of problems depends on the geometry of the domain. The authors give estimates for some problems of this kind in the case when they have positive solutions and analyze in depth the case of the unit ball.

MSC:

35J40 Boundary value problems for higher-order elliptic equations
35J35 Variational methods for higher-order elliptic equations
35B45 A priori estimates in context of PDEs
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