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Linear parabolic equations in locally uniform spaces. (English) Zbl 1058.35076
The authors initiate the study of semigroups generated by second-order elliptic operators on uniform \(L^p\)-spaces. They analyze the heat semigroup on these spaces, develop some perturbation theory by potentials, obtain \(L^p\)-\(L^q\) estimates and estimate the type of the semigroups. They also study the semigroups generated by second-order non-divergence type differential operators assuming some regularity of the coefficients.

MSC:
35K15 Initial value problems for second-order parabolic equations
47D06 One-parameter semigroups and linear evolution equations
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