Abstract:We consider the mixed Dirichlet-conormal problem for the heat equation on cylindrical domains with a bounded and Lipschitz base Ω ⊂ R d and a time-dependent separation Λ. Under certain mild regularity assumptions on Λ, we show that for any q > 1 sufficiently close to 1, the mixed problem in L q is solvable. In other words, for any given Dirichlet data in the parabolic Riesz potential space L 1 q and the Neumann data in L q , there is a unique solution and the non-tangential maximal function of its gradient is … Show more
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