Su un teorema di unicità per l'equazione semilineare del calore in un dominio illimitato

Bassanini, Piero

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 78 (1985) no. 6, pp. 278-285

Résumé

A periodic BVP for a semilinear elliptic-parabolic equation in an unbounded domain $\Omega$ contained in a half-space of $\mathbb{R}^{n}$ is considered, with Dirichlet boundary conditions on the finite part of $\partial \Omega$. A theorem of uniqueness of periodic solutions is proved by showing that a suitable function of the "energy" $E(x)$ is subharmonic in $\Omega$ and satisfies a Phragmèn-Lindelöf growth condition at infinity.