Heat kernel estimates and functional calculi of −bΔ
DOI:
https://doi.org/10.7146/math.scand.a-14310Abstract
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.Downloads
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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