Higher Integrability for Parabolic Systems with Non-standard Growth and Degenerate

  title={Higher Integrability for Parabolic Systems with Non-standard Growth and Degenerate},
  author={Verena B{\"o}gelein and Frank Duzaar},
(1.1) ∂tu− div a(z,Du) = div ( |F |p(z)−2F ) in ΩT . Here, ΩT denotes the space time cylinder Ω × (0, T ) over a bounded domain Ω ⊆ R with dimension n ≥ 2. We write z = (x, t) for points in R, Du for the spatial gradient of u and ∂tu for the derivative with respect to time. The function u : ΩT → R with N ≥ 1 can possibly be vector valued, so that we include in our considerations the case of parabolic systems. The precise structural assumptions on the vector-field a and the exponent function p… CONTINUE READING

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