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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 28, Issue 2


Second order elliptic operators with diffusion coefficients growing as |x|α at infinity

Motohiro Sobajima
  • Department of Mathematics, Tokyo University of Science, Japan; and Department of Mathematics and Physics “Ennio De Giorgi”, University of Salento, C.P. 193, 73100, Lecce, Italy
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/ Chiara Spina
Published Online: 2015-01-11 | DOI: https://doi.org/10.1515/forum-2014-0055


We prove that, for N/(N-2) < p < ∞, α > 2, the operator Lu = (1 + |x|2)α/2Tr(A(x)D2u) = (1 + |x|2)α/2i,j=1,...,N aij(x)Diju admits realizations generating analytic semigroups in Lp(ℝN). Moreover, for α < N/p', we provide an explicit description of the domain.

Keywords: Elliptic operators; unbounded coefficients; generation results; analytic semigroups

MSC: 47D07; 35B50; 35J25; 35J70

About the article

Received: 2014-03-28

Revised: 2014-07-18

Published Online: 2015-01-11

Published in Print: 2016-03-01

Citation Information: Forum Mathematicum, Volume 28, Issue 2, Pages 391–402, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2014-0055.

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G. Metafune, M. Sobajima, and C. Spina
Annali di Matematica Pura ed Applicata (1923 -), 2016, Volume 195, Number 4, Page 1305

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