Optimal Hölderregularity for nonautonomous Kolmogorov equations

Luca Lorenzi

doi:10.3934/dcdss.2011.4.169

Article Contents

2011, Volume 4, Issue 1: 169-191. Doi: 10.3934/dcdss.2011.4.169

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Optimal Hölder regularity for nonautonomous Kolmogorov equations

Luca Lorenzi^1,

1.
Dipartimento di Matematica, Università degli Studi di Parma, Viale Parco Area delle Scienze 53/A, I-43124 Parma

Received: January 31, 2009

Revised: September 30, 2009

Published: January 2011

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Abstract

We consider a class of nonautonomous elliptic operators A with unbounded coefficients defined in $[0,T]\times\R^N$ and we prove optimal Schauder estimates for the solution to the parabolic Cauchy problem $D_tu=$A$u+g$, $u(0,\cdot)=f$.

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Mathematics Subject Classification: Primary: 35B65; Secondary: 35K15, 35R05.

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