$L^p$-regularity for elliptic operators with unbounded coefficients

By Giorgio Metafune, Jan Prüss, Roland Schnaubelt, Abdelaziz Rhandi. Advances in Differential Equations, 2005

67 citations recorded by the source corpus.

Abstract. Under suitable conditions on the functions a ∈ C(R , RN2), F ∈ C(R , R ), and V : R → [0,∞), we show that the operator Au = ∇(a∇u) + F · ∇u − V u with domain W 2,p V (R ) = {u ∈ W (R ) : V u ∈ L(R )} generates a positive analytic semigroup on L(R ), 1 < p < ∞. Analogous results are also established in the spaces L(R ) and C0(R ). As an application we show that the generalized Ornstein–Uhlenbeck operator AΦ,Gu = ∆u − ∇Φ · ∇u + G · ∇u with domain W (R , μ) generates an analytic semigroup on the weighted space L(R , μ), where 1 < p < ∞ and μ(dx) = e−Φ(x)dx.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/80a33c48da23efcb10aa34a9fa6d9d97bea00b1d

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In Applied Mathematics

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1. Luca Lorenzi
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3. Markus Kunze

Citations in the corpus

• Estimates of the derivatives for parabolic operators with unbounded coefficients (2005, methodology): “There are just a few results in the particular case when the drift term is a gradient (see [16]) or A is an Ornstein-Uhlenbeck operator (see [15]).”