In this paper we consider the Cauchy problem for the heat equation with a nonnegative potential decaying quadratically at the space infinity and investigate local concavity properties of the solution. In particular, we give a sufficient condition for the solution to be quasi-concave in a ball for any sufficiently large t, and discuss the optimality of the sufficient condition, identifying a threshold for the occurrence of local quasi-concavity. © 2011 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.
Local quasi-concavity of the solutions of the heat equation with a nonnegative potential / Andreucci, Daniele; Kazuhiro, Ishige. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 192:3(2013), pp. 329-348. [10.1007/s10231-011-0226-x]
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Titolo: | Local quasi-concavity of the solutions of the heat equation with a nonnegative potential | |
Autori: | ||
Data di pubblicazione: | 2013 | |
Rivista: | ||
Citazione: | Local quasi-concavity of the solutions of the heat equation with a nonnegative potential / Andreucci, Daniele; Kazuhiro, Ishige. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 192:3(2013), pp. 329-348. [10.1007/s10231-011-0226-x] | |
Handle: | http://hdl.handle.net/11573/434841 | |
Appartiene alla tipologia: | 01a Articolo in rivista |