Operators in the Calculus of Variations

24 Abril 2019, 15:30 • José Francisco da Silva Costa Rodrigues

General variational inequalities for operators in the Calculus of Variations—existence in the case of pseudomonotone and coercive operators. Discussion of the concept of pseudomonotonicity and its relations with monotonicity, semicontinuity and the M-property. Their role in the proof of the existence of a solution to general variational inequalities by approximation of solutions in finite dimensional subspaces—extension of the Galerkin method. Examples of potential operators in reflexive Banach spaces and operators of the type of the Calculus of variations in the sense of Leray-Lions and their applications to quasi-linear elliptic operators with certain symmetry and growth properties of their coefficients.


Further reading: [L69]-J.L.Lions, Quelques méthodes de résolution de problèmes aux limites non linéaires, Junod, Paris, 1969 (namely Sections 2 and 8 of Chap. 2)

Exercises 2.83 (page 75), 4.22+4.23+4.24 (page127) of Roubicek's 2013 book.

Lecture: 26-4-2919—14:00/17:30