Ishige, Kazuhiro; Salani, Paolo On a new kind of convexity for solutions of parabolic problems. (English) Zbl 1223.35188 Discrete Contin. Dyn. Syst., Ser. S 4, No. 4, 851-864 (2011). 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.]. Cited in 1 ReviewCited in 14 Documents MSC: 35K20 Initial-boundary value problems for second-order parabolic equations 52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces) 35K59 Quasilinear parabolic equations Keywords:\(\alpha\)-parabolic quasi-concavity Citations:Zbl 1206.35020 PDFBibTeX XMLCite \textit{K. Ishige} and \textit{P. Salani}, Discrete Contin. Dyn. Syst., Ser. S 4, No. 4, 851--864 (2011; Zbl 1223.35188) Full Text: DOI