Abstract
We study a nonlinear parabolic equation with an irregular obstacle over a non-smooth domain and establish a global Calderón–Zygmund theory by proving that the spatial gradient of the weak solution is as integrable as both that of the obstacle and the nonhomogeneous term. Our results extend the known interior regularity for such obstacle problems in Lebesgue spaces to the boundary one in Orlicz spaces. The domain under consideration is a δ-Reifenberg domain which is a natural extension of a Lipschitz one with a small Lipschitz constant, while the function space under consideration is an Orlicz space which is a natural generalization of the Lebesgue space.
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This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (MEST) (2009-0083521).
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Byun, SS., Cho, Y. Nonlinear gradient estimates for parabolic obstacle problems in non-smooth domains. manuscripta math. 146, 539–558 (2015). https://doi.org/10.1007/s00229-014-0707-5
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DOI: https://doi.org/10.1007/s00229-014-0707-5