Gaussian estimates for fundamental solutions of second order parabolic systems with time-independent coefficients

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Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on ℝn. In particular, in the case when n = 2 they obtained Gaussian upper bound estimates for the heat kernel without imposing further assumption on the coefficients. We study the fundamental solutions of the systems of second order parabolic equations in the divergence form with bounded, measurable, time-independent coefficients, and extend their results to the systems of parabolic equations.

Original languageEnglish
Pages (from-to)6031-6043
Number of pages13
JournalTransactions of the American Mathematical Society
Issue number11
Publication statusPublished - 2008 Nov 1


All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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