Global optimal regularity for the parabolic polyharmonic equations.

Yao, Fengping

Displaying similar documents to “Global optimal regularity for the parabolic polyharmonic equations.”

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Inspired by a problem in steel metallurgy, we prove the existence, regularity, uniqueness, and continuous data dependence of solutions to a coupled parabolic system in a smooth bounded 3D domain, with nonlinear and nonhomogeneous boundary conditions. The nonlinear coupling takes place in the diffusion coefficient. The proofs are based on anisotropic estimates in tangential and normal directions, and on a refined variant of the Gronwall lemma.

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We discuss the convergence of approximate identities in Musielak-Orlicz spaces extending the results given by Cruz-Uribe and Fiorenza (2007) and the authors F.-Y. Maeda, Y. Mizuta and T. Ohno (2010). As in these papers, we treat the case where the approximate identity is of potential type and the case where the approximate identity is defined by a function of compact support. We also give a Young type inequality for convolution with respect to the norm in Musielak-Orlicz spaces. ...

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Embedding theorems in Banach-valued $B$ -spaces and maximal $B$ -regular differential-operator equations.

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Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents

Yan Lu, Yue Ping Zhu (2014)

Czechoslovak Mathematical Journal

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We introduce a new type of variable exponent function spaces $M {\dot{K}}_{q, p (\cdot)}^{α (\cdot), λ} (ℝ^{n})$ of Morrey-Herz type where the two main indices are variable exponents, and give some propositions of the introduced spaces. Under the assumption that the exponents $α$ and $p$ are subject to the log-decay continuity both at the origin and at infinity, we prove the boundedness of a wide class of sublinear operators satisfying a proper size condition which include maximal, potential and Calderón-Zygmund operators and their commutators...