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, p. 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 : 2018-06-21
Classification:  47D07,  35B50,  35J25,  35J70
@article{ASNSP_2012_5_11_2_303_0,
     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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 11},
     number = {2},
     year = {2012},
     pages = {303-340},
     zbl = {1264.47048},
     mrnumber = {3011993},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2012_5_11_2_303_0}
}
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://www.numdam.org/item/ASNSP_2012_5_11_2_303_0/

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