Following the approach in our earlier paper [2] and using the gradient estimates developed in [2] and [3], we give another Liouville type theorem for some conformally invariant fully nonlinear equations. Various Liouville type theorems for conformally invariant equations have been obtained by Obata, Gidas-Ni-Nirenberg, CaffarelliGidas-Spruck, Viaclovsky, Chang-Gursky-Yang, and Li-Li. For these,...

We consider the Dirichlet problem for semilinear elliptic equations on a smooth bounded domain Ω. We assume that Ω is symmetric about a hyperplane H and convex in the direction orthogonal to H. Employing Serrin’s result on an overdetermined problem, we show that any nonzero nonnegative solution is necessarily strictly positive. One can thus apply a well-known result of Gidas, Ni and Nirenberg t...

We describe several topics within the theory of linear and nonlinear second order elliptic Partial Differential Equations. Through elementary approaches, we first explain how elliptic and parabolic PDEs are related to central issues in Probability and Geometry. This leads to several concrete equations. We classify them and describe their regularity theories. After this, most of the paper focuse...

Let g : R 7→ R be a locally Lipschitz continuous function and BR(0) the open N -ball (N ≥ 2) of center 0 and radius R > 0. A classical result due to Gidas, Ni and Nirenberg [4] asserts that any positive solution u of (1) −∆u+ g(u) = 0 in BR(0) which vanishes on ∂BR(0) is radial. A conjecture proposed by H. Brezis is that any large solution of (1), that is a solution which verifies (2) lim |x|→R...

We prove radial symmetry for bounded nonnegative solutions of a weighted anisotropic problem. Given the setting that we deal with, term "radial" is understood in Finsler framework. In whole space, J. Serra obtained result isotropic unweighted setting. this case provide extension his to This provides generalization celebrated due Gidas-Ni-Nirenberg and such new even linear operators whenever dim...

در این تحقیق به مقایسه تحلیلی و عددی آبشار جریان برگشتی مدل R با آبشارهای Q QI سیستم‌­های چندجزیی پایدار پرداخته می‌­شود. راستا برای اولین بار کدهای جهت طراحی منظور کد نرم‌افزار متلب نوشته شده‌­اند. نتایج نشان می‌­دهد که دو جزء 1k 2k از خوراک Nc جزء، تعداد معدودی قابل تعریف است همگی حالات خاصی می­‌باشد. هم‌­چنین یافته‌­ها مجموع مقدار برش جزیی همیشه برابر یک است. طریق داده می‌­شود صورتی میانگین ...

In this paper, we study some new connections between Liouville-type theorems and local properties of nonnegative solutions to superlinear elliptic problems. Namely, we develop a general method for derivation of universal, pointwise a priori estimates of local solutions from Liouville-type theorems, which provides a simpler and unified treatment for such questions. The method is based on rescali...

This paper aims at investigating brain injury mechanisms in adult pedestrian accidents by indepth accident analysis and accident reconstructions. In total, 120 adult pedestrian accident cases from the GIDAS database were analysed and 10 of them were reconstructed. The accident reconstructions were first carried out using multi-body system (MBS) pedestrian and car models to acquire the head impa...

A simple, but realistic, model of an autonomous emergency brake (AEB) system was studied. Using Matlab, the model was applied to 543 car‐to‐pedestrian and 607 car‐to‐bicyclist real‐world collisions gathered from the highly detailed German In‐Depth Accident Study Pre‐Crash Matrix (GIDAS PCM) and weighted for representativeness. All collisions were to the front of the car. The aim was ...