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• W2024951358 abstract "Let [Formula: see text] be a second order, uniformly elliptic, positive semi-definite differential operator on a complete Riemannian manifold of bounded geometry M, acting between sections of a vector bundle with bounded geometry E over M. We assume that the coefficients of L are uniformly bounded. Using finite speed of propagation for L, we investigate properties of operators of the form [Formula: see text]. In particular, we establish results on the distribution kernels and mapping properties of e -tL and (μ + L) s . We show that L generates a holomorphic semigroup that has the usual mapping properties between the W s,p -Sobolev spaces on M and E. We also prove that L satisfies maximal L p –L q -regularity for 1 < p, q < ∞. We apply these results to study parabolic systems of semi-linear equations of the form ∂ t u + Lu = F(t, x, u, ∇ u)." @default.
• W2024951358 created "2016-06-24" @default.
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• W2024951358 date "2006-12-01" @default.
• W2024951358 modified "2023-10-05" @default.
• W2024951358 title "MAPPING PROPERTIES OF HEAT KERNELS, MAXIMAL REGULARITY, AND SEMI-LINEAR PARABOLIC EQUATIONS ON NONCOMPACT MANIFOLDS" @default.
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• W2024951358 doi "https://doi.org/10.1142/s0219891606000938" @default.
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