Gaussian estimates and instantaneous blowup

Goldstein J. A., KÖMBE İ.

Positivity, vol.12, no.1, pp.75-82, 2008 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 1
  • Publication Date: 2008
  • Doi Number: 10.1007/s11117-007-2105-7
  • Journal Name: Positivity
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.75-82
  • Keywords: Gaussian estimates, Heat equation, Instantaneous blowup, Non-symmetric elliptic operator, Singular potential
  • İstanbul Ticaret University Affiliated: Yes

Abstract

For L a second order linear elliptic differential operator on ℝN, one is usually interested in finding positive solutions of the heat equation u\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. © 2007 Birkhäuser Verlag Basel/Switzerland.