Gaussian Estimates and Instantaneous Blowup

Gaussian Estimates and Instantaneous Blowup For L a second order linear elliptic differential operator on $${\mathbb{R}}^N$$ , one is usually interested in finding positive solutions of the heat equation $$\frac{\partial u}{\partial {t}}=Lu+Vu,$$ where V is a nonnegative potential. But for L the Laplacian, it was discovered by [BG] in 1984 that positive solutions may not exist if V is too singular. We use Gaussian estimates to extend this result to the case when L is not symmetric. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Gaussian Estimates and Instantaneous Blowup

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Publisher
Birkhäuser-Verlag
Copyright
Copyright © 2007 by Birkhäuser Verlag Basel/Switzerland
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-007-2105-7
Publisher site
See Article on Publisher Site

Abstract

For L a second order linear elliptic differential operator on $${\mathbb{R}}^N$$ , one is usually interested in finding positive solutions of the heat equation $$\frac{\partial u}{\partial {t}}=Lu+Vu,$$ where V is a nonnegative potential. But for L the Laplacian, it was discovered by [BG] in 1984 that positive solutions may not exist if V is too singular. We use Gaussian estimates to extend this result to the case when L is not symmetric.

Journal

PositivitySpringer Journals

Published: Oct 29, 2007

References

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