Nonlinear obstacle problems with double phase in the borderline case

In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with $(p,q)$-growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.     

Time‐dependent finite element simulations of a shear‐thinning viscoelastic fluid with application to blood flow

A new finite element method is developed to simulate time‐dependent viscoelastic shear‐thinning flows characterized by the generalized Oldroyd‐B model. The focus of the algorithm is improved stability through a free‐energy dissipative scheme by using low‐order piecewise‐constant finite element approximations for stress. The algorithm is further modified by incorporating a pressure‐projection method, a DG‐upwinding scheme, a symmetric interior penalty DG method to solve the elliptic pressure‐update equation and a geometric multigrid preconditioner. The improved stability and cost to accuracy is compared when using higher order discontinuous bilinear approximation, where in addition, we consider the influence of a slope limiter for these elements. The algorithm is applied to the 2D start‐up‐driven cavity problem, and the stability of the free energy is illustrated and compared between element choices. An application of the model to modelling blood in small arterioles and channels is considered by simulating pulsatile blood flow through a stenotic arteriole. The individual influences of viscoelasticity and shear‐thinning within the generalized Oldroyd‐B model are investigated by comparing results to the Newtonian, generalized Newtonian and Oldroyd‐B models. Copyright © 2014 John Wiley & Sons, Ltd.     

Development and validation of a simple solid‐phase extraction method coupled with liquid chromatography–triple quadrupole tandem mass spectrometry for simultaneous determination of lincomycin,tylosin A and tylosin B in royal jelly

We have developed an analytical method for the determination of lincomycin, tylosin A and tylosin B residues in royal jelly using liquid chromatography–triple quadrupole tandem mass spectrometry analysis. For extraction and purification, we employed 1% trifluoroacetic acid and 0.1 m Na₂EDTA solutions along with an Oasis HLB cartridge. The target antibiotics were well separated in a Kinetex EVO C₁₈ reversed‐phase analytical column using a combination of 0.1% formate acid in ultrapure water (A) and acetonitrile (B) as the mobile phase. Good linearity was achieved over the tested concentration range (5–50 μg/kg) in matrix‐matched standard calibration. The coefficients of determination (R²) were 0.9933, 0.9933 and 0.996, for tylosin A, tylosin B and lincomycin, respectively. Fortified royal jelly spiked with three different concentrations of the tested antibiotics (5, 10 and 20 μg/kg) yielded recoveries in the range 80.94–109.26% with relative standard deviations ≤4%. The proposed method was applied to monitor 11 brand of royal jelly collected from domestic markets and an imported brand from New Zealand; all the samples tested negative for lincomycin, tylosin A and tylosin B residues. In conclusion, 1% trifluoroacetic acid and 0.1 m Na₂EDTA aqueous solvents combined with solid‐phase extraction could effectively complete the sample preparation process for royal jelly before analysis. The developed approach can be applied for a routine analysis of lincomycin, tylosin A and tylosin B residues in royal jelly.     

Interior estimates for the n-dimensional Abreuʼs equation

We study the Abreu?s equation in n-dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform K-stability.     

Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.     

Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.