Two Generalizations of Stampacchia Lemma and Applications

We present two generalizations of the classical Stampacchia Lemma which contain a non-decreasing non-negative function $g$, and give applications. As a first application, we deal with variational integrals of the form $${\cal J} (u;\Omega) = \int_{\Omega}\ f(x,Du{(x)})dx.$$ We consider a minimizer $u: \Omega \subset \mathbb R^n \to \mathbb R$ among all functions with a fixed boundary value $u_{\ast }$ on $\partial \Omega$. Under some nonstandard growth conditions of the integrand $f(x,\xi)$ we derive some regularity results; as a second application, we consider elliptic equations of the form \begin{cases} -\mbox {div} \left( a(x, u(x)) D u(x) \right) = f(x), & x \in \Omega, u(x) = 0, & x \in {\partial \Omega}, \end{cases} under the conditions $$\frac {\alpha }{(1+|s|) ^\theta \ln ^\theta (e+|s|)} \le a (x,s) \le \beta, \ \ \ 0<\alpha \le \beta <\infty, \ \theta \ge 0,$$ we obtain some regularity properties of its weak solutions.Comment: 26 page

Integrability for Solutions of Anisotropic Obstacle Problems

This paper deals with anisotropic obstacle problem for the -harmonic equation ∑i=1nDi(ai(x,Du(x)))=0. An integrability result is given under suitable assumptions, which show higher integrability of the boundary datum, and the obstacle force solutions u have higher integrability as well

Applications of Fixed Point Theorems to Generalized Saddle Points of Bifunctions on Chain-Complete Posets

We apply the extensions of the Abian-Brown fixed point theorem for set-valued mappings on chain-complete posets to examine the existence of generalized and extended saddle points of bifunctions defined on posets. We also study the generalized and extended equilibrium problems and the solvability of ordered variational inequalities on posets, which are equipped with a partial order relation and have neither an algebraic structure nor a topological structure

Immune-inflammatory biomarkers for the occurrence of MACE in patients with myocardial infarction with non-obstructive coronary arteries

BackgroundNeutrophil-to-high-density lipoprotein cholesterol ratio (NHR), monocyte-to-high-density lipoprotein cholesterol ratio (MHR), lymphocyte-to-high-density lipoprotein cholesterol ratio (LHR), platelet-to-high-density lipoprotein cholesterol ratio (PHR), systemic immune-inflammation index (SII), systemic inflammation response index (SIRI), and aggregate index of systemic inflammation (AISI) have been identified as immune-inflammatory biomarkers associated with the prognosis of cardiovascular diseases. However, the relationship of these biomarkers with the prognosis of myocardial infarction with non-obstructive coronary arteries (MINOCA) remains unclear.MethodPatients with MINOCA who underwent coronary angiography at the 920th Hospital of Joint Logistics Support Force were included in our study. Clinical baseline characteristics and laboratory testing data were collected from the hospital record system. The patients were divided into two groups on the basis of major adverse cardiovascular events (MACE) occurrence. Multiple logistic regression analysis was conducted to assess the relationship between NHR, MHR, LHR, PHR, SII, SIRI, AISI, and MACE. Receiver operating characteristic (ROC) curves were generated to evaluate the predictive value of NHR, MHR, LHR, PHR, SII, SIRI, and AISI for MACE in patients with MINOCA. The accuracy of the prediction was indicated by the area under the curve (AUC) value.ResultsThe study included 335 patients with MINOCA. (81 in the MACE group and 254 in the No-MACE group). The MACE group had higher levels of NHR, MHR, LHR, PHR, SII, SIRI, and AISI than the No-MACE group. Multiple logistic regression analysis adjusted for confounding factors indicated that the higher levels of NHR, MHR, PHR, SII, SIRI, and AISI were associated with the occurrence of MACE in patients with MINOCA (P &lt; 0.001). The AUC values for NHR, MHR, PHR, SII, SIRI, and AISI were 0.695, 0.747, 0.674, 0.673, 0.688, and 0.676, respectively. The combination of NHR, MHR, PHR, SII, SIRI, and AISI improved the accuracy of predicting MACE in patients with MINOCA (AUC = 0.804).ConclusionHigher levels of NHR, MHR, PHR, SII, SIRI, and AISI were associated with the occurrence of MACE, and the combination of NHR, MHR, PHR, SII, SIRI, and AISI improved the accuracy for predicting the incidence of MACE events in patients with MINOCA

Weighted integral inequalities for conjugate A-harmonic tensors

AbstractWe first prove a local weighted integral inequality for conjugate A-harmonic tensors. Then, as an application of our local result, we prove a global weighted integral inequality for conjugate A-harmonic tensors in Ls(μ)-averaging domains, which can be considered as a generalization of the classical result. Finally, we give applications of the above results to quasiregular mappings

New weighted poincar&#233;-type inequalities for differential forms

<p/> <p>We first prove local weighted Poincar&#233;-type inequalities for differential forms. Then, by using the local results, we prove global weighted Poincar&#233;-type inequalities for differential forms in John domains, which can be considered as generalizations of the classical Poincar&#233;-type inequality.</p

A1(Ω)-Weighted Caccioppoli-Type Inequality for A-Harmonic Tensors *

In this paper, we first obtain a local A1(Ω)-weighted Caccioppolitype inequality for A-harmonic tensors, then as an application of our local result, we prove a global A1(Ω)-weighted Caccioppoli-type inequality. These results can be considered as generalizations of the classical results