Cipriani, Fabio; Grillo, Gabriele Pointwise lower bounds for positive solutions of elliptic equations and applications to intrinsic ultracontractivity of Schrödinger semigroups. (English) Zbl 0888.35019 Boll. Unione Mat. Ital., VII. Ser., B 10, No. 4, 927-941 (1996). The authors prove a decay estimate for positive solutions of linear elliptic equations. The estimate is based on the Harnack inequality and on the quasi-hyperbolic metric. For similar results see [F. W. Gehring and O. Martio, Ann. Acad. Sci. Fenn., Ser. A I Math. 10, 203-219 (1985; Zbl 0584.30018)] and [M. Vuorinen, Ann. Acad. Sci. Fenn., Ser. A I Math. 7, 259-277 (1982; Zbl 0505.31003)]. They also apply the methods to study intrinsic ultracontractivity connected with Schrödinger operators. Reviewer: O.Martio (Helsinki) MSC: 35B45 A priori estimates in context of PDEs 35J25 Boundary value problems for second-order elliptic equations 35J10 Schrödinger operator, Schrödinger equation 47D03 Groups and semigroups of linear operators Keywords:decay estimate; Harnack inequality; intrinsic ultracontractivity Citations:Zbl 0584.30018; Zbl 0505.31003 PDFBibTeX XMLCite \textit{F. Cipriani} and \textit{G. Grillo}, Boll. Unione Mat. Ital., VII. Ser., B 10, No. 4, 927--941 (1996; Zbl 0888.35019)