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

In: Functional Analysis and Evolution Equations

Author

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  • Luca Lorenzi

    (Università degli Studi di Parma, Dipartimento di Matematica)

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.

Suggested Citation

  • Luca Lorenzi, 2007. "On a Class of Elliptic Operators with Unbounded Time- and Space-dependent Coefficients in ℝ N," Springer Books, in: Herbert Amann & Wolfgang Arendt & Matthias Hieber & Frank M. Neubrander & Serge Nicaise & Joachim vo (ed.), Functional Analysis and Evolution Equations, pages 433-456, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7643-7794-6_28
    DOI: 10.1007/978-3-7643-7794-6_28
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