The penalty method for variational inequalities with nonsmooth unbounded operators in Banach space. (English) Zbl 0867.49009

Summary: We study the existence of a solution and convergence and stability of the penalty method for variational inequalities with nonsmooth unbounded uniformly and properly monotone operators in a Banach space. All the objects of the inequality – the operator, “the data” and the set of constraints – are to be perturbed. The stability theorems are formulated in terms of geometric characteristics of the space and its dual. The results of this paper extend and generalize results of J. L. Lions [“Quelques méthodes de résolution des problèmes aux limites non linéaires” (1969; Zbl 0189.40603)]. They are new even in Hilbert spaces.


49J40 Variational inequalities
47J25 Iterative procedures involving nonlinear operators
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49M30 Other numerical methods in calculus of variations (MSC2010)


Zbl 0189.40603
Full Text: DOI arXiv


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