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 language | English |
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Pages (from-to) | 481-496 |
Number of pages | 16 |
Journal | Publicacions Matematiques |
Volume | 48 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2004 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)