We prove that, for , , , the operator generates an analytic semigroup in which is contractive if and only if . Moreover, for , we provide an explicit description of the domain. Spectral properties of the operator are also obtained.
@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}, 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://archive.numdam.org/item/ASNSP_2012_5_11_2_303_0/} }
TY - JOUR AU - Metafune, Giorgio AU - Spina, Chiara TI - Elliptic operators with unbounded diffusion coefficients in $L^p$ spaces JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 303 EP - 340 VL - 11 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2012_5_11_2_303_0/ LA - en ID - ASNSP_2012_5_11_2_303_0 ER -
%0 Journal Article %A Metafune, Giorgio %A Spina, Chiara %T Elliptic operators with unbounded diffusion coefficients in $L^p$ spaces %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 303-340 %V 11 %N 2 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2012_5_11_2_303_0/ %G en %F 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://archive.numdam.org/item/ASNSP_2012_5_11_2_303_0/
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