Search results for "Regularity"

Multiple solutions for (p,2)-equations at resonance

2019

We consider a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a p-Laplacian and a Laplacian and a reaction term which is (p− 1)-linear near ±∞ and resonant with respect to any nonprincipal variational eigenvalue of (−∆p, W01,p(Ω)). Using variational tools together with truncation and comparison techniques and Morse Theory (critical groups), we establish the existence of six nontrivial smooth solutions. For five of them we provide sign information and order them.

Weak chord-arc curves and double-dome quasisymmetric spheres

2014

Let $\Omega$ be a planar Jordan domain and $\alpha>0$. We consider double-dome-like surfaces $\Sigma(\Omega,t^{\alpha})$ over $\overline{\Omega}$ where the height of the surface over any point $x\in\overline{\Omega}$ equals $\text{dist}(x,\partial\Omega)^{\alpha}$. We identify the necessary and sufficient conditions in terms of $\Omega$ and $\alpha$ so that these surfaces are quasisymmetric to $\mathbb{S}^2$ and we show that $\Sigma(\Omega,t^{\alpha})$ is quasisymmetric to the unit sphere $\mathbb{S}^2$ if and only if it is linearly locally connected and Ahlfors $2$-regular.

Nonlinear elliptic equations with asymmetric asymptotic behavior at $pminfty$

2016

We consider a nonlinear, nonhomogeneous Dirichlet problem with reaction which is asymptotically superlinear at $+infty$ and sublinear at $-infty$. Using minimax methods together with suitable truncation techniques and Morse theory, we show that the problem has at least three nontrivial solutions one of which is negative.

Characterization of the Clarke regularity of subanalytic sets

2017

International audience; In this note, we will show that for a closed subanalytic subset $A \subset \mathbb{R}^n$, the Clarke tangential regularity of $A$ at $x_0 \in A$ is equivalent to the coincidence of the Clarke's tangent cone to $A$ at $x_0$ with the set \\$$\mathcal{L}(A, x_0):= \bigg\{\dot{c}_+(0) \in \mathbb{R}^n: \, c:[0,1]\longrightarrow A\;\;\mbox{\it is Lipschitz}, \, c(0)=x_0\bigg\}.$$Where $\dot{c}_+(0)$ denotes the right-strict derivative of $c$ at $0$. The results obtained are used to show that the Clarke regularity of the epigraph of a function may be characterized by a new formula of the Clarke subdifferential of that function.

Evaluation of menstrual irregularities after COVID-19 vaccination: Results of the MECOVAC survey

2022

Abstract We investigated menstrual irregularities after the first and second doses of the COVID-19 vaccine. Women answered a customised online questionnaire (ClinicalTrial.gov ID: NCT05083065) aimed to assess the vaccine type, the phase of the menstrual cycle during which the vaccine was administered, the occurrence of menstrual irregularities after the first and second doses, and how long this effect lasted. We excluded women with gynaecological and non-gynaecological diseases, undergoing hormonal and non-hormonal treatments, in perimenopause or menopause, as well as those who had irregular menstrual cycles in the last 12 months before vaccine administration. According to our data analysis…

INTERNAL AUDIT: DEFINING, OBJECTIVES, FUNCTIONS AND STAGES

2010

This article aims, through a detailed presentation as to provide clarification for a better understanding of what internal audit definition, objectives, functions and stages of its development mean. It is also exposed a brief history about the emergence and development of internal audit and regulatory framework. I also plan to linking theory and practice by reference to documents used: both the evidence considered and especially those prepared by the auditors in connection with the performance audit and its use in the audit report.

C1,α regularity for the normalized p-Poisson problem

2017

We consider the normalized p -Poisson problem − Δ N p u = f in Ω ⊂ R n . The normalized p -Laplacian Δ N p u := | Du | 2 − p Δ p u is in non-divergence form and arises for example from stochastic games. We prove C 1 ,α loc regularity with nearly optimal α for viscosity solutions of this problem. In the case f ∈ L ∞ ∩ C and p> 1 we use methods both from viscosity and weak theory, whereas in the case f ∈ L q ∩ C , q> max( n, p 2 , 2), and p> 2 we rely on the tools of nonlinear potential theory peerReviewed

2021

The purpose of this study was to investigate the prevalence of self-reported restrictive eating, current or past eating disorder, and menstrual dysfunction and their relationships with injuries. Furthermore, we aimed to compare these prevalences and associations between younger (aged 15–24) and older (aged 25–45) athletes, between elite and non-elite athletes, and between athletes competing in lean and non-lean sports. Data were collected using a web-based questionnaire. Participants were 846 female athletes representing 67 different sports. Results showed that 25%, 18%, and 32% of the athletes reported restrictive eating, eating disorders, and menstrual dysfunction, respectively. Higher ra…

(p,2)-equations resonant at any variational eigenvalue

2018

We consider nonlinear elliptic Dirichlet problems driven by the sum of a p-Laplacian and a Laplacian (a (p,2) -equation). The reaction term at ±∞ is resonant with respect to any variational eigenvalue of the p-Laplacian. We prove two multiplicity theorems for such equations.

Solutions with sign information for nonlinear Robin problems with no growth restriction on reaction

2019

We consider a parametric nonlinear Robin problem driven by a nonhomogeneous differential operator. The reaction is a Carathéodory function which is only locally defined (that is, the hypotheses concern only its behaviour near zero). The conditions on the reaction are minimal. Using variational tools together with truncation, perturbation and comparison techniques and critical groups, we show that for all small values of the parameter λ > 0, the problem has at least three nontrivial smooth solutions, two of constant sign and the third nodal.