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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.
Positivity – Springer Journals
Published: Oct 29, 2007
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