On a Class of Elliptic Operators with Unbounded Time- and Space-dependent Coefficients in ℝ N

Luca Lorenzi ()
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Luca Lorenzi: Università degli Studi di Parma, Dipartimento di Matematica

A chapter in Functional Analysis and Evolution Equations, 2007, pp 433-456 from Springer

Abstract: Abstract We prove optimal Schauder estimates for classical solutions of the nonhomogeneous Cauchy problem associated with a class of elliptic operators with unbounded coefficients depending both on time and space variables. We deal both with the case when the coefficients of the elliptic operator are continuous and the case when they are merely measurable in the pair (t, x). In both the cases we assume that they are Hölder continuous in x, uniformly with respect to t.

Keywords: Linear parabolic equations in ℝ N with unbounded and measurable coefficients; Cauchy problems; Schauder estimates (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7643-7794-6_28

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DOI: 10.1007/978-3-7643-7794-6_28

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