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

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13 Citations (Scopus)

Abstract

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
Volume360
Issue number11
DOIs
Publication statusPublished - 2008 Nov 1

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Gaussian Estimates
Second-order Systems
Parabolic Systems
Fundamental Solution
Heat Kernel
Parabolic Equation
Divergence
Coefficient
Second Order Equations
Elliptic Operator
Upper bound
Estimate
Hot Temperature
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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