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.
Reviewer: A. Salvadori


49J27 Existence theories for problems in abstract spaces
49J45 Methods involving semicontinuity and convergence; relaxation
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
47H05 Monotone operators and generalizations