A probabilistic approach to the boundedness of singular integral operators

Regularity results for elliptic systems of second order quasilinear PDEs with nonlinear growth of order $q > 2$ are proved, extending results of [7] and [10]. In particular Hölder regularity of the solutions is obtained if the dimension $n$ is less than or equal to $q + 2$ .

On a new weighted Hilbert inequality.

Leping, He, Xuemei, Gao, Mingzhe, Gao (2008)

Journal of Inequalities and Applications [electronic only]

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Regularity results for a class of obstacle problems

Michela Eleuteri (2007)

Applications of Mathematics

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We prove some optimal regularity results for minimizers of the integral functional $\int f (x, u, D u) d x$ belonging to the class $K : = {u \in W^{1, p} (Ω) u \geq ψ}$ , where $ψ$ is a fixed function, under standard growth conditions of $p$ -type, i.e. $L^{- 1} {| z |}^{p} \leq f (x, s, z) \leq {L (1 + | z |}^{p}) .$

A Hilbert integral-type inequality with parameters.

Xiaozhou, Shang, Mingzhe, Gao (2010)

International Journal of Mathematics and Mathematical Sciences

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On new extensions of Hilbert's integral inequality.

Leping, He, Mingzhe, Gao, Yu, Zhou (2008)

International Journal of Mathematics and Mathematical Sciences

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