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On a new kind of convexity for solutions of parabolic problems. (English) Zbl 1223.35188

Summary: We introduce the notion of \(\alpha\)-parabolic quasi-concavity for functions of space and time, which extends the usual notion of quasi-concavity and the notion of parabolic quasi-cocavity introduced in [the authors, Math. Nachr. 283, No. 11, 1526–1548 (2010; Zbl 1206.35020)]. Then we investigate the \(\alpha\)-parabolic quasi-concavity of solutions to parabolic problems with vanishing initial datum. The results here obtained are generalizations of some of the results of [loc. cit.].

MSC:

35K20 Initial-boundary value problems for second-order parabolic equations
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
35K59 Quasilinear parabolic equations

Citations:

Zbl 1206.35020
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