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Pointwise lower bounds for positive solutions of elliptic equations and applications to intrinsic ultracontractivity of Schrödinger semigroups. (English) Zbl 0888.35019

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.

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
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