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H\"{o}lder continuity of solutions to the $G$-Laplace equation

Jun Zheng; Yan ZhangSubjects: Mathematics >> Mathematics （General）

We establish regularity of solutions to the $G$-Laplace equation $-\text{div}\ \bigg(\frac{g(|\nabla u|)}{|\nabla u|}\nabla u\bigg)=\mu$, where $\mu$ is a nonnegative Radon measure satisfying $\mu (B_{r}(x_{0}))\leq Cr^{m}$ for any ball $B_{r}(x_{0})\subset\subset \Omega$ with $r\leq 1$ and $m>n-1-\delta\geq 0$. The function $g(t)$ is supposed to be nonnegative and $C^{1}$-continuous in $[0,+\infty)$, satisfying $g(0)=0$, and for some positive constants $\delta$ and $g_{0}$, $\delta\leq \frac{tg'(t)}{g(t)}\leq g_{0}, \forall t>0$, that generalizes the structural conditions of Ladyzhenskaya-Ural'tseva for an elliptic operator. |

submitted time
2018-09-22
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Study of $B \to K_0^*(1430)K^(*)$ decays in QCD Factorization Approach

Ying Li; Hong-Yan Zhang; Ye Xing; Zuo-Hong Li; Cai-Dian L╱Subjects: Physics >> Nuclear Physics

Within the QCD factorization approach, we calculate the branching fractions and?CP?asymmetry parameters of 12?B→K?0(1430)K(?)?decay modes under the assumption that the scalar meson?K?0(1430)?is the first excited state or the lowest lying ground state in the quark model. We find that the decay modes with the scalar meson emitted, have large branching fractions due to the enhancement of large chiral factor?rK?0χ. The branching fractions of decays with the vector meson emitted, become much smaller owing to the smaller factor?rK?χ. Moreover, the annihilation type diagram will induce large uncertainties because of the extra free parameter dealing with the endpoint singularity. For the pure annihilation type decays, our predictions are smaller than that from PQCD approach by 2-3 orders of magnitudes. These results will be tested by the ongoing LHCb experiment, forthcoming Belle-II experiment and the proposing circular electron-positron collider. |

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