We consider a class of functionals of the calculus of variations which are not strictly convex in the gradient of the function. When critical point theory is applied, this causes some troubles with the Palais-Smale condition, which we overcome using a suitable nonsmooth approach.
Degiovanni, M., Variational methods for functionals with lack of strict convexity, in Nonlinear equations: methods, models and applications, (Bergamo, 09-13 July 2001), Birkhaeuser, Boston 2003: 127-139 [https://hdl.handle.net/10807/312910]
Variational methods for functionals with lack of strict convexity
Degiovanni, Marco
2003
Abstract
We consider a class of functionals of the calculus of variations which are not strictly convex in the gradient of the function. When critical point theory is applied, this causes some troubles with the Palais-Smale condition, which we overcome using a suitable nonsmooth approach.
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