Landesman-Lazer type results for second order Hamilton-Jacobi-Bellman equations

We extend the classical Landesman-Lazer results to the setting of second order Hamilton-Jacobi-Bellman equations. A number of new phenomena appear

Solvability of nonlinear elliptic equations with gradient terms

We study the solvability in the whole Euclidean space of coercive quasi-linear and fully nonlinear elliptic equations modeled on $\Delta u\pm g(|\nabla u|)= f(u)$, $u\ge0$, where $f$ and $g$ are increasing continuous functions. We give conditions on $f$ and $g$ which guarantee the availability or the absence of positive solutions of such equations in $\R^N$. Our results considerably improve the existing ones and are sharp or close to sharp in the model cases. In particular, we completely characterize the solvability of such equations when $f$ and $g$ have power growth at infinity. We also derive a solvability statement for coercive equations in general form

Solvability of monotone systems of fully nonlinear elliptic PDE's

International audienceWe study quasimonotone systems of fully nonlinear uniformly elliptic equations. Our goal is, on one hand, to give a necessary and sufficient condition under which the system satisfies a comparison principle, and on the other hand, to give explicit conditions under which ordered sub- and supersolutions can be found, so Perron's method implies the existence of a solution. For a large class of systems our results are optimal. Further, we aim at proving results of existence of eigenvalues of vector fully nonlinear operators

On the principal eigenvalues and the Dirichlet problem for fully nonlinear operators

We study uniformly elliptic fully nonlinear equations of the type$F(D^2u, Du, u, x)=f(x)$. We show that convex positively 1-homogeneous operators possess two principal eigenvalues and eigenfunctions, and study these objects ; obtain existence and uniqueness results for non-proper operators whose principal eigenvalues (in some cases, only one of them) are positive ; obtain an existence result for non-proper Isaac's equations

Evaluation of multidetector CT Hounsfield unit measurements as a predictor of efficacy and complications in percutaneous vertebroplasty for osteoporotic vertebral compression fractures

IntroductionMore than 30 years after the initial experience of Galibert and Deramond with percutaneous vertebroplasty, the procedure has gone through countless refinements and clinical evaluations. Predictors for the success and failure of the procedure in the literature vary and are focused on the duration of complaints, type of fracture, presence of edema on MRI scans, etc. We propose using a quantitative method based on a standard CT examination of the thoracic or lumbar spine to assess the risks and potential success of performing vertebroplasty.Materials and methodsThis is a single-center prospective observational study on 139 patients treated with percutaneous vertebroplasty (pVPL) for a single symptomatic osteoporotic vertebral compression fracture (OVCF). We measured the levels of disability and pain preoperatively and again at the 3-, 6- and 12-month marks using the standardized VAS and ODI questionnaires. Every patient in the study was evaluated with postoperative multidetector CT (MDCT) to determine the presence, extent, and localization of vertebral cement leakage and to measure the adjacent vertebrae’s minimal and mean density in Hounsfield units (HUmin and HUmean, respectively).ResultsWe determined that a slight (r = −0.201) but statistically significant (p = 0.018) correlation existed between HU measurements taken from radiologically intact adjacent vertebrae and the procedure’s effect concerning the pain levels at the 3-month follow-up. This correlation failed to reach statistical significance at 12 months (p = 0.072). We found no statistically significant relationship between low vertebral cancellous bone density and cement leakage on postoperative scans (p = 0.6 for HUmin and p = 0.74 for HUmean).ConclusionWe have moderately strong data that show a negative correlation between the mean values of vertebral cancellous bone density in patients with OVCF and the effect of pVPL in reducing pain. Lower bone densities, measured this way, showed no increased risk of cement leakage

Principal eigenvalues and the Dirichlet problem for fully nonlinear elliptic operators

Abstract. We study uniformly elliptic fully nonlinear equations of the type F (D2u, Du, u, x) = f(x). We show that convex positively 1-homogeneous operators possess two principal eigenvalues and eigenfunctions, and study these objects; we obtain existence and uniqueness results for non-proper operators whose principal eigenvalues (in some cases, only one of them) are positive; finally, we obtain an existence result for non-proper Isaac’s equations. 2000 Mathematics Subject Classification: 35J60, 35J65, 35P30. 1 Introduction and Main Results This paper is a study of uniformly elliptic fully nonlinear equations in nondivergence form F (D 2 u, Du, u, x) = f(x) (1.1) in a bounded domain Ω ⊂ R N. We pursue the following goals. First, we sho

Developmental venous anomaly causing obstructive hydrocephalus due to aqueductal stenosis: а case report

Cerebral developmental venous anomalies are asymptomatic benign cerebrovascular malformations that are commonly found accidentally on brain magnetic resonance imaging. It is not uncommon for cerebrospinal fluid flow to be obstructed at the level of the aqueduct of Sylvius, causing an obstructive non-communicating hydrocephalus. Most notable reasons for such an obstruction at that level are tumors, congenital etiology, or post-inflammatory gliotic atresia. Herein we present the case of a 65-year-old male patient with an unusual symptomatic developmental venous anomalies causing stenosis and obstruction of the aqueduct of Sylvius at the level of the mesencephalon. Features of this case are discussed together with its implications, including recognizing, diagnosing, and treating such a finding

Critical Angiographic and Sonographic Analysis of Intra Aneurysmal and Downstream Hemodynamic Changes After Flow Diversion

IntroductionSuccessful treatment of intracranial aneurysms after flow diversion (FD) is dependent on the flow modulating effect of the device. We aimed to investigate the intra-aneurysmal and parent vessel hemodynamic changes, as well as the incidence of silent emboli following treatment with various FD devices.MethodsWe evaluated the appearance of the eclipse sign in nine distinct phases of cerebral angiography before and immediately after FD placement in correlation with aneurysm occlusion. Angiographic and clinical data of consecutive procedures were analyzed retrospectively. Patients who had successful FD procedure without adjunctive coiling, visible eclipse sign on post embolization angiography, and reliable follow-up angiographic data were included in the analysis. Detailed analysis of hemodynamic data from transcranial doppler after FD was performed in selected patients, such as monitoring for silent emboli.ResultsAmong all patients (N = 65) who met inclusion criteria, complete aneurysm occlusion at 12 months was achieved in 89% (58/65). Eclipse sign prior to FD was observed in 42% (27/65) with unchanged appearance in 4.6% (3/65) of the treated patients. None of these three patients achieved complete aneurysm occlusion. Among all analyzed variables, such as aneurysm size, device type used, age, and appearance of the eclipse sign pre- and post-FD, the most reliable predictor of permanent aneurysm occlusion at 12 months was earlier, prolonged, and sustained eclipse sign visibility in more than three angiographic phases in comparison to the baseline (p < 0.001). Elevation in flow velocities within the ipsilateral vascular territory was noted in 70% (9/13), and bilaterally in 54% (7/13) of the treated patients. None of the patients had silent emboli.ConclusionsIntra-aneurysmal and parent vessel hemodynamic changes after FD can be reliably assessed by the cerebral angiography and transcranial doppler with important implications for the prediction of successful treatment

Diversion-p64: results from an international, prospective, multicenter, single-arm post-market study to assess the safety and effectiveness of the p64 flow modulation device

International audienceBackground: The use of flow diversion to treat intracranial aneurysms has increased in recent years.Objective: To assess the safety and angiographic efficacy of the p64 flow modulation device.Methods: Diversion-p64 is an international, prospective, multicenter, single-arm, study conducted at 26 centers. The p64 flow modulation device was used to treat anterior circulation aneurysms between December 2015 and January 2019. The primary safety endpoint was the incidence of major stroke or neurologic death at 3-6 months, with the primary efficacy endpoint being complete aneurysm occlusion (Raymond-Roy Occlusion Classification 1) on follow-up angiography.Results: A total of 420 patients met the eligibility criteria and underwent treatment with the p64 flow modulation device (mean age 55±12.0 years, 86.2% female). Mean aneurysm dome width was 6.99±5.28 mm and neck width 4.47±2.28 mm. Mean number of devices implanted per patient was 1.06±0.47, with adjunctive coiling performed in 14.0% of the cases. At the second angiographic follow-up (mean 375±73 days), available for 343 patients (81.7%), complete aneurysm occlusion was seen in 287 (83.7%) patients. Safety data were available for 413 patients (98.3%) at the first follow-up (mean 145±43 days) with a composite morbidity/mortality rate of 2.42% (n=10).Conclusions: Diversion-p64 is the largest prospective study using the p64 flow modulation device. The results of this study demonstrate that the device has a high efficacy and carries a low rate of mortality and permanent morbidity