Weak limits of Palais-Smale sequences for a class of critical functionals
Let \(F\) be a functional defined on a Hilbert space \(M\). The author states that in many interesting cases Palais-Smale sequences in \(M\) do not necessarily converge strongly to a critical point for \(F\). Therefore it is very important to prove that Palais-Smale sequences converge weakly to a critical point. Here the author studies the problem of surfaces of prescribed mean curvature and the related Palais-Smale sequences and extends the method to the harmonic map equation. For this purpose the author gives some preliminary results on isoperimetric inequality, Coarea formulas etc. followed by approximation theorem and a technique for computing boundary terms.
scientific article; zbMATH DE number 509959
scientific article