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Evolution equations associated with $$(p,q)$$-convex functions and $$(p,q)$$-monotone operators. (English) Zbl 0582.49005
The notions of $$(p,q)$$-convex functions and $$(p,q)$$-monotone operators introduced by E. De Giorgi, A. Marino and M. Tosques [Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 73, 6-14 (1982; Zbl 0521.49011)] are very useful in order to deal with some evolution problems, in the case that nonconvex unilateral constraints are considered (see e.g. A. Marino and D. Scolozzi [Boll. Unione Mat. Ital., VI. Ser., B 6, 1–31 (1983; Zbl 0567.35005)]). In the present paper the authors continue and complete the study they already started in a previous paper [Ric. Mat. 32, 285–319 (1983; Zbl 0555.49007)], where they proved many general properties of these objects. In particular, here they give some existence theorems for evolution equations associated with $$(p,q)$$-monotone operators, moreover they deal with the $$\Gamma$$-convergence of $$(p,q)$$-convex functions.