Evolution equations associated with \((p,q)\)-convex functions and \((p,q)\)-monotone operators. (English) Zbl 0582.49005

Degiovanni, Marco; Marino, Antonio; Tosques, Mario

Ric. Mat. 33, 81-112 (1984).

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

MSC:

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

Keywords:

gamma convergence; (p,q)-convex functions; (p,q)-monotone operators; existence theorems for evolution equations

Citations:

Zbl 0521.49011; Zbl 0567.35005; Zbl 0555.49007