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On the parabolic kernel of the Schrödinger operator
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In this paper, we will study parabolic equations of the typeon a general Riemannian manifold.The function q(x, t) is assumed to be C 2 in the first variable and C 1 in the second variable.In classical situations [20], a Harnack inequality for positive solutions was established locally.However, the geometric dependency of the estimates is complicated and sometimes unclear.Our goal is to prove a Harnack inequality for positive solutions of (0.1) (w 2) by utilizing a gradient estimate derived in w 1.The method of proof is originated in [26] and [8], where they have studied the elliptic case, i.e. the solution is time independent.In some situations (Theorems 2.2 and
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Chow, B., & Knopf, D. (2004) · Mathematical Surveys and Monographs · doi:10.1090/surv/110 · Cited by 579
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Grigor'yan, A., & Saloff-Coste, L. (2005) · Annales de l'Institut Fourier · doi:10.5802/aif.2116 · Cited by 99
Green's functions, harmonic functions, and volume comparison
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Metadata
- Authors
- Li, P., & Yau, S. T.
- Venue
- Acta Mathematica
- Publisher
- International Press of Boston
- Published
- 1986
- Volume
- 156
- Issue
- 0
- Pages
- 153-201
- ISSN
- 0001-5962 (ISSN-L)
- OpenAlex
- W1970224775
- Cited by
- 1,446
- References
- 0
- FWCI
- 11.07
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Li, P., & Yau, S. T. (1986). On the parabolic kernel of the Schrödinger operator. Acta Mathematica. https://doi.org/10.1007/bf02399203
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