Gaussian estimates for fundamental solutions to certain parabolic systems

• Autores: Steve Hofmann, Seick Kim
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 48, Nº 2, 2004, págs. 481-496
• Idioma: español
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• Resumen

  • 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.