Gaussian estimates for fundamental solutions to certain parabolic systems

Steve Hofmann, Seick Kim

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Auscher proved Gaussian upper bound estimates for the fundamental solutions to parabolic equations with complex coefficients in the case when coefficients are time-independent and a small perturbation of real coefficients. We prove the equivalence between the local boundedness property of solutions to a parabolic system and a Gaussian upper bound for its fundamental matrix. As a consequence, we extend Auscher's result to the time dependent case.

Original languageEnglish
Pages (from-to)481-496
Number of pages16
JournalPublicacions Matematiques
Volume48
Issue number2
DOIs
Publication statusPublished - 2004 Jan 1

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Gaussian Estimates
Parabolic Systems
Fundamental Solution
Coefficient
Upper bound
Fundamental Matrix
Small Perturbations
Parabolic Equation
Boundedness
Equivalence
Estimate

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Gaussian estimates for fundamental solutions to certain parabolic systems. / Hofmann, Steve; Kim, Seick.

In: Publicacions Matematiques, Vol. 48, No. 2, 01.01.2004, p. 481-496.

Research output: Contribution to journalArticle

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