Abstract
The main aspects in nonsmooth critical point theory are discussed throughout this chapter, namely the notion of critical point for functionals which are not differentiable, but are locally Lipschitz, a sum between C 1-functional and a convex l.s.c. functional or, more general, the sum between a locally Lipschitz and a convex l.s.c. functional. Various compactness conditions, ensuring that every sequence for which the functional is converging to a critical value has a convergent subsequence, are also presented. The Principle of Symmetric Criticality for C 1-functionals and its extensions to locally Lipschitz and Szulkin functionals are also discussed; these results are particularly import in the discussion of nonsmooth elliptic PDEs defined on unbounded domains with certain symmetries.
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Costea, N., Kristály, A., Varga, C. (2021). Critical Points, Compactness Conditions and Symmetric Criticality. In: Variational and Monotonicity Methods in Nonsmooth Analysis. Frontiers in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-81671-1_3
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DOI: https://doi.org/10.1007/978-3-030-81671-1_3
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