Bubbling phenomena of Palais-Smale-like sequences of \(m\)-harmonic type systems
The Palais-Smale condition for a functional \(E\) is a natural assumption for the existence of a critical point of \(E\). In many interesting cases the Palais-Smale condition fails due to the phenomena called bubbling. This failure of strong convergence is due to the loss of energy. Using a renormalization procedure to construct bubbles the authors describe in their main theorem the convergence behaviour of certain weakly convergent sequences and account for all the energy loss with a finite number of bubbles. Then they apply their result to \(m\)-harmonic maps to a Riemannian homogeneous space and to \(m\)-harmonic maps with a constant volume.
scientific article; zbMATH DE number 898031
scientific article