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For a fixed bounded Lipschitz domain and a family of systems of linear elasticity with rapidly oscillating periodic coefficients, we investigate a necessary and sufficient condition that an A 1 weight ω must satisfy in order for the weighted W 1 , 2 (ω) estimates for weak solutions of Neumann problems to be true. Moreover, in any Lipschitz domain, under the assumption that the coefficient A is Hölder continuous, we prove that the uniform W 1 , p estimates for solutions to the Neumann problem hold for 2 d d + 1 − δ < p < 2 d d − 1 + δ. As a by-product, in non-periodic setting with A ∈ V M O , we are able to show that the W 1 , p estimates hold for 2 d d + 1 − δ < p < 2 d d − 1 + δ. The ranges are sharp for d = 2 , 3. Finally, we prove an extrapolation result for L p Dirichlet problems for systems of linear elasticity. Specifically, we extrapolate from solvability for 1 < p 0 < 2 (d − 1) d − 2 to the range p 0 < p < 2 (d − 1) d − 2 + δ. The novelty is that the method avoids using the L 2 regularity estimate. [ABSTRACT FROM AUTHOR]

For a family of second-order parabolic systems in divergence form with rapidly oscillating periodic and time-dependent coefficients. We establish the pointwise estimates of the Green's matrices. We investigate uniform boundary Lipschitz estimates and boundary Hölder estimates as well as non-tangential maximum function estimates in C 1 , η or C 1 cylinders. Consequently, we also obtain the Agmon-Miranda maximum principle. [ABSTRACT FROM AUTHOR]

The primary purpose of this paper is to investigate a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization in Lipschitz domains. As a consequence, for d ≥ 4 , we prove that the L p Neumann and L p Dirichlet boundary value problems for systems of second order linear elasticity are uniquely solvable for 2 ( d − 1 ) d + 1 − δ < p < 2 + δ and 2 − δ < p < 2 ( d − 1 ) d − 3 + δ respectively. [ABSTRACT FROM AUTHOR]

For a family of second-order parabolic systems with bounded measurable, rapidly oscillating and time-dependent periodic coefficients, we investigate the sharp convergence rates of weak solutions in L 2 . Both initial-Dirichlet and initial-Neumann problems are studied. [ABSTRACT FROM AUTHOR]

We study the L p regularity problem for the stationary Stokes system on Lipschitz domains. For any p > 2 we show that a weak reverse Hölder inequality with exponent p is both necessary and sufficient for the solvability of the regularity problem with data in W 1 , p ( ∂ Ω ) ∩ L n p ( ∂ Ω ) . We also obtain the W 1 , p ( Ω ) estimate ‖ ∇ u ‖ L p ( Ω ) + ‖ q ‖ L p ( Ω ) ≤ ‖ f ‖ L p ( Ω ) in a bounded Lipschitz domain Ω ⊂ R d for solutions to the Dirichlet problem Δ u = ∇ q + div ( f ) , div ( u ) = 0 in Ω and u = 0 on ∂Ω, where | 1 p − 1 2 | < 1 2 d + ε . [ABSTRACT FROM AUTHOR]

Abstract: We study estimates in Lipschitz domains for second order elliptic equations and systems of divergence form with real-valued, bounded, measurable coefficients. For any fixed , we prove that a weak reverse Hölder inequality implies the estimates for solutions with Neumann boundary conditions. As a result, we are able to show that if the coefficient matrix of elliptic equation is symmetric and in , the estimate holds for if , and for if , and for elliptic systems the estimate is true for . [Copyright &y& Elsevier]

Abstract: Let be a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients. We obtain the uniform estimate in a Lipschitz domain Ω in for solutions to the Dirichlet problem: in Ω and on ∂Ω, where and C, are constants independent of . The ranges are sharp for or 3. [Copyright &y& Elsevier]

Abstract: We show that the Neumann problem for Laplace''s equation in a convex domain Ω with boundary data in is uniquely solvable for . As a consequence, we obtain the Helmholtz decomposition of vector fields in . [Copyright &y& Elsevier]

• The mortality of older adult patients was higher than the younger adult patients. • All scores had good predictive value in both older and younger adult patients. • END-IT**** is the most suitable scoring tool for patients under 65. • EMSE-EAL*** is the most suitable scoring tool for patients over 65. The goal of this study was to evaluate the predictive capacity of four scoring tools: the Status Epilepticus Severity Score (STESS), the Encephalitis-NCSE-Diazepam resistance-Image abnormalities-Tracheal intubation (END-IT) score, and two variable combinations of the Epidemiology-based Mortality Score in Status Epilepticus (EMSE) in younger and older adult patients with status epilepticus (SE). We present a retrospective hospital-based analysis with a focus on adult patients with SE at three tertiary care hospitals in the Zhejiang province of China. Data were collected from January 2013 to December 2018. The patients were divided into two groups: younger adult patients (18–64 years old) and older adult patients (≥65 years old). Clinical outcomes (dead or alive) were assessed at hospital discharge. The four scoring tools were used to predict in-hospital mortality in both younger and older adult patients. The mortality rate in older adult patients (25.4%) was higher than in younger adult patients (12.9%). Compared with the elderly, the younger adult patients had a higher proportion of encephalitis, while acute cerebrovascular disease and Charlson Complications Index (CCI) were lower. For the younger adult patients, END-IT had the largest area under the curve (AUC) of 0.843 (95% CI, 0.772–0.899), which was higher than the EMSE-EAL value of 0.687 (95% CI, 0.603–0.763, p < 0.05) and EMSE-EAC of 0.646 (95% CI, 0.561–0.725, p < 0.05). For the older adult patients, EMSE-EAL had the largest AUC of 0.843 (95% CI, 0.738–0.919), which was significantly higher than STESS with an AUC of 0.676 (95% CI, 0.554–0.782, p < 0.05). Moreover, the AUC of EMSE-EAL in the elderly was larger than in younger adult patients. The cutoffs in younger adult patients were STESS ≥ 4 (sensitivity 0.444, specificity 0.951), END-IT ≥ 3 (sensitivity 0.833, specificity 0.672), EMSE-EAL ≥ 31 (sensitivity 0.778, specificity 0.566), and EMSE-EAC ≥ 33 (sensitivity 0.833, specificity 0.492). However, the cutoffs in older adult patients were STESS ≥ 5 (sensitivity 0.500, specificity 0.925), END-IT ≥ 2 (sensitivity 0.944, specificity 0.547), EMSE-EAL ≥ 30 (sensitivity 0.944, specificity 0.623), and EMSE-EAC ≥ 31 (sensitivity 0.944, specificity 0.415). Our results indicated that the STESS, END-IT, EMSE-EAC, and EMSE-EAL scores have excellent capacity to predict in-hospital mortality in both younger and older adult patients with SE. Our study supports the use of END-IT in patients under 65 years of age and suggests that EMSE-EAL is the most suitable scoring tool for patients over 65. [ABSTRACT FROM AUTHOR]