Search results for "app"

Hölder gradient regularity for the inhomogeneous normalized p(x)-Laplace equation

2022

We prove the local gradient Hölder regularity of viscosity solutions to the inhomogeneous normalized p(x)-Laplace equation −Δp(x)Nu=f(x), where p is Lipschitz continuous, inf⁡p>1, and f is continuous and bounded. peerReviewed

Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian

2018

In this paper, we study an evolution equation involving the normalized [Formula: see text]-Laplacian and a bounded continuous source term. The normalized [Formula: see text]-Laplacian is in non-divergence form and arises for example from stochastic tug-of-war games with noise. We prove local [Formula: see text] regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration.

Regularity for nonlinear stochastic games

2015

We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding partial differential equations. peerReviewed

Remarks on regularity for p-Laplacian type equations in non-divergence form

2018

We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of viscosity solutions in the full range $\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\gamma$ is close to 0.

Ultrasound-guided viscosupplementation in glenohumeral microinstability in sports athletes

2014

Fractional Hardy inequalities and visibility of the boundary

2013

We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection to the boundedness of extension operators for fractional Sobolev spaces.

Extraction d'un graphe de navigabilité à partir d'un nuage de points 3D enrichis

2017

International audience; Ce travail se place dans le cadre général du projet ANR pLaTINUM lié à la navigation autonome et plus parti-culièrement à la génération de cartes pour la navigation basée perception. Il consiste à développer une nouvelle méthode pour résumer une carte 3D (un nuage dense de points 3D) et extraire un graphe de navigabilité facilitant l'utilisation de cette carte par des systèmes de navigation à ressources matérielles limitées (smart-phones, voitures, robots.. .). Cette méthode vise à ex-traire les régions les plus saillantes de l'environnement étudié afin de construire une carte récapitulative. Ce processus de résumé de carte basé sur la vision est appliqué d'une façon…

Cluster visual field progression and its relationship with optic disc changes

2015

Purpose Glaucoma diagnosis and follow up of progression is often based on structural and functional assessments. This study aimed to assess clustered progression and evaluate its correlation with the corresponding disc changes (RA sectors) obtained from HRT examinations. Methods 51 eyes from OHT and glaucoma patients with a minimum of 5 reliable visual ᴀ밄eld tests (HFA II i 24-2) and HRT with a follow-up >4 years were analyzed retrospectively. Linear regression of clusters deᴀ밄ned by the Glaucoma Hemiᴀ밄eld Test (GHT) was performed based on the mean threshold in each cluster. Global and sectoral rates of change in RAs were assessed and correlated with functional clustered measures. Cluste…

AnatomySketch : An Extensible Open-Source Software Platform for Medical Image Analysis Algorithm Development

2021

AbstractThe development of medical image analysis algorithm is a complex process including the multiple sub-steps of model training, data visualization, human–computer interaction and graphical user interface (GUI) construction. To accelerate the development process, algorithm developers need a software tool to assist with all the sub-steps so that they can focus on the core function implementation. Especially, for the development of deep learning (DL) algorithms, a software tool supporting training data annotation and GUI construction is highly desired. In this work, we constructed AnatomySketch, an extensible open-source software platform with a friendly GUI and a flexible plugin interfac…

Reperti su alcuni Artropodi fitofagi in colture di rilevente interesse economico in Sicilia.

2001