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.
In memory of Günter Lumer
Work partially supported by the research project “Kolmogorov equations” of the Ministero dell’Istruzione, dell’Università e della Ricerca (M.I.U.R).
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Lorenzi, L. (2007). On a Class of Elliptic Operators with Unbounded Time- and Space-dependent Coefficients in ℝN . In: Amann, H., Arendt, W., Hieber, M., Neubrander, F.M., Nicaise, S., von Below, J. (eds) Functional Analysis and Evolution Equations. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7794-6_28
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DOI: https://doi.org/10.1007/978-3-7643-7794-6_28
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