Heat kernel estimates and functional calculi of bΔ

Authors

  • Alan McIntosh
  • Andrea Nahmod

DOI:

https://doi.org/10.7146/math.scand.a-14310

Abstract

We show that the elliptic operator L=b(x)Δ has a bounded H functional calculus in Lp(Rn),1<p<, where b is a bounded measurable complex-valued function with positive real part. In the process, we prove quadratic estimates for L, and obtain bounds with fast decay and Hölder continuity estimates for kt(x,y)b(y) and its gradient, where kt(x,y) is the heat kernel of b(x)Δ. This implies Lp regularity of solutions to the parabolic equation tu+Lu=0.

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Published

2000-12-01

How to Cite

McIntosh, A., & Nahmod, A. (2000). Heat kernel estimates and functional calculi of bΔ. MATHEMATICA SCANDINAVICA, 87(2), 287–319. https://doi.org/10.7146/math.scand.a-14310

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Section

Articles