Gradient estimates for parabolic and elliptic systems from linear laminates

Details Gradient estimates for parabolic and elliptic systems from linear laminates Gradient estimates for parabolic and elliptic systems from linear laminates

2012-01-24

arxiv.org/abs/1201.5146v1

Mathematics

Analysis of PDEs

31 pages, submitted in Jan. 2011, to appear in ARMA

Scientific paper

10.1007/s00205-012-0501-z

We establish several gradient estimates for second-order divergence type parabolic and elliptic systems. The coefficients and data are assumed to be H\"older or Dini continuous in the time variable and all but one spatial variables. This type of systems arises from the problems of linearly elastic laminates and composite materials. For the proof, we use Campanato's approach in a novel way. Non-divergence type equations under a similar condition are also discussed.

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