Elliptic operators with unbounded diffusion coefficients in Lp spaces

By Giorgio Metafune, C. Spina. 2010

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In this paper we prove that, under suitable assumptions on {\alpha} > 0, the operator L = (1 + |x|{\alpha})\Delta admits realizations generating contraction or analytic semigroups in Lp (RN). For some values of {\alpha}, we also explicitly characterize the domain of L. Finally, some informations about the location and composition of the spectrum are given.

View Paper: https://www.semanticscholar.org/paper/e1a0034990be605f1bc6fd1ec72c1e03cdea77b4