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Here $W_t$ is a one-dimensional Wiener process on a probability space $\\Omega$. It has been proved (see below for references) that for any $p\\geq 2$ the inequality $$ \\|\\nabla u\\|_{L_p(\\Omega\\times [0,T]\\times D)} \\leq c \\|g\\|_{L_p(\\Omega\\times [0,T]\\times D)} $$ holds if $\\partial D\\in C^1$. 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