Elliptic operators with unbounded diffusion coefficients in L p spaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 2, pp. 303-340.

We prove that, for N3, α>2, N N-2<p<, the operator Lu=m(x)(1+|x| α )Δu generates an analytic semigroup in L p which is contractive if and only if pN+α-2 N-2. Moreover, for α<N p ' , we provide an explicit description of the domain. Spectral properties of the operator L are also obtained.

Published online:
Classification: 47D07, 35B50, 35J25, 35J70
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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Metafune, Giorgio; Spina, Chiara. Elliptic operators with unbounded diffusion coefficients in $L^p$ spaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 2, pp. 303-340. http://archive.numdam.org/item/ASNSP_2012_5_11_2_303_0/

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