Elliptic operators with unbounded diffusion coefficients in $L^p$ spaces

Metafune, Giorgio; Spina, Chiara

Elliptic operators with unbounded diffusion coefficients in

L^{p}

spaces

Metafune, Giorgio ¹ ; Spina, Chiara ¹

¹ Dipartimento di Matematica “Ennio De Giorgi” Università del Salento C.P. 193 73100, Lecce, Italia

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 2, pp. 303-340.

Résumé

We prove that, for $N \geq 3$ , $α > 2$ , $\frac{N}{N - 2} < p < \infty$ , the operator $L u = m (x) (1 + | x |^{α}) Δ u$ generates an analytic semigroup in $L^{p}$ which is contractive if and only if $p \geq \frac{N + α - 2}{N - 2}$ . Moreover, for $α < \frac{N}{p^{'}}$ , we provide an explicit description of the domain. Spectral properties of the operator $L$ are also obtained.

Publié le : 2018-06-21

MR Zbl

Classification : 47D07, 35B50, 35J25, 35J70

Affiliations des auteurs :

Metafune, Giorgio ¹ ; Spina, Chiara ¹

¹ Dipartimento di Matematica “Ennio De Giorgi” Università del Salento C.P. 193 73100, Lecce, Italia

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     author = {Metafune, Giorgio and Spina, Chiara},
     title = {Elliptic operators with unbounded diffusion coefficients in $L^p$ spaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {303--340},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 11},
     number = {2},
     year = {2012},
     mrnumber = {3011993},
     zbl = {1264.47048},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2012_5_11_2_303_0/}
}

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Metafune, Giorgio; Spina, Chiara. Elliptic operators with unbounded diffusion coefficients in $L^p$ spaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 2, pp. 303-340. http://www.numdam.org/item/ASNSP_2012_5_11_2_303_0/

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