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Admissible and regular potentials for positive \(C_ 0\)-semigroups and application to heat semigroups. (English) Zbl 0817.47050

The author solves the following initial value problem given by the heat equation by using the semi-group theory \[ u_ t= {\textstyle {1\over 2}} \Delta u- V_ u, \qquad u(0)= u_ 0. \] The main tool in the investigation is the Voigt’s perturbation theory of positive \(C_ 0\)- semigroups in \(L^ p\) spaces where \(1\leq p<\infty\).

MSC:

47D06 One-parameter semigroups and linear evolution equations
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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