The eigenvalue problem for the ∞-Bilaplacian

We consider the problem of finding and describing minimisers of the Rayleigh quotient Λ∞:=infu∈W2,∞(Ω)∖{0}∥Δu∥L∞(Ω)∥u∥L∞(Ω), Λ∞:=infu∈W2,∞(Ω)∖{0}‖Δu‖L∞(Ω)‖u‖L∞(Ω), where Ω⊆RnΩ⊆Rn is a bounded C1,1C1,1 domain and W2,∞(Ω)W2,∞(Ω) is a class of weakly twice differentiable functions satisfying either u=0u=0 on ∂Ω∂Ω or u=|Du|=0u=|Du|=0 on ∂Ω∂Ω . Our first main result, obtained through approximation by LpLp -problems as p→∞p→∞ , is the existence of a minimiser u∞∈W2,∞(Ω)u∞∈W2,∞(Ω) satisfying {Δu∞∈Λ∞Sgn(f∞)Δf∞=μ∞ a.e. in Ω, in D′(Ω), {Δu∞∈Λ∞Sgn(f∞) a.e. in Ω,Δf∞=μ∞ in D′(Ω), for some f∞∈L1(Ω)∩BVloc(Ω)f∞∈L1(Ω)∩BVloc(Ω) and a measure μ∞∈M(Ω)μ∞∈M(Ω) , for either choice of boundary conditions. Here Sgn is the multi-valued sign function. We also study the dependence of the eigenvalue Λ∞Λ∞ on the domain, establishing the validity of a Faber–Krahn type inequality: among all C1,1C1,1 domains with fixed measure, the ball is a strict minimiser of Ω↦Λ∞(Ω)Ω↦Λ∞(Ω) . This result is shown to hold true for either choice of boundary conditions and in every dimension

Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.Comment: To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 201

The prescribed mean curvature equation in weakly regular domains

We show that the characterization of existence and uniqueness up to vertical translations of solutions to the prescribed mean curvature equation, originally proved by Giusti in the smooth case, holds true for domains satisfying very mild regularity assumptions. Our results apply in particular to the non-parametric solutions of the capillary problem for perfectly wetting fluids in zero gravity. Among the essential tools used in the proofs, we mention a \textit{generalized Gauss-Green theorem} based on the construction of the weak normal trace of a vector field with bounded divergence, in the spirit of classical results due to Anzellotti, and a \textit{weak Young's law} for $(\Lambda,r_{0})$-minimizers of the perimeter.Comment: 23 pages, 1 figure --- The results on the weak normal trace of vector fields have been now extended and moved in a self-contained paper available at: arXiv:1708.0139

Impact of long-term elosulfase alfa treatment on respiratory function in patients with Morquio A syndrome

OBJECTIVE: To present long-term respiratory function outcomes from an open-label, multi-center, phase 3 extension study (MOR-005) of elosulfase alfa enzyme replacement therapy (ERT) in patients with Morquio A syndrome. METHODS: In part 1 of MOR-005, patients initially randomized to ERT in the 24-week pivotal study (MOR-004) remained on their regimen (2.0 mg/kg/week or every other week); placebo patients were re-randomized to one of the two regimens. During part 2, all patients received elosulfase alfa 2.0 mg/kg/week. Respiratory function was one of the efficacy endpoints evaluated in MOR-005. Change from MOR-004 baseline to 120 weeks of treatment for the combined population was determined and compared with results from untreated patients from a Morquio A natural history study (MorCAP). RESULTS: Maximum voluntary ventilation (MVV) improved up to week 72 and then stabilized; forced vital capacity (FVC) and forced expiratory volume in 1 s (FEV1) increased continuously over 120 weeks. Mean increases in the modified per-protocol population was 9.2 % for FVC, 8.8 % for FEV1, and 6.1 % for MVV after 120 weeks. All patients ≤14 years showed respiratory improvements, presumably in part related to growth; however, these were greater in treated patients. For those >14 years, treated patients showed improvements, while deterioration occurred in untreated. Altogether, the improvements were significantly greater (P < 0.05) in treated patients. CONCLUSIONS: Long-term ERT is associated with sustained improvements in respiratory function in Morquio A. In younger patients (≤14 years), some improvement may be ascribed to growth. In older patients, other mechanisms, e.g., decreased glycosaminoglycan storage, are likely involved

Intestinal PPARγ signalling is required for sympathetic nervous system activation in response to caloric restriction.

Nuclear receptor PPARγ has been proven to affect metabolism in multiple tissues, and has received considerable attention for its involvement in colon cancer and inflammatory disease. However, its role in intestinal metabolism has been largely ignored. To investigate this potential aspect of PPARγ function, we submitted intestinal epithelium-specific PPARγ knockout mice (iePPARγKO) to a two-week period of 25% caloric restriction (CR), following which iePPARγKO mice retained more fat than their wild type littermates. In attempting to explain this discrepancy, we analysed the liver, skeletal muscle, intestinal lipid trafficking, and the microbiome, none of which appeared to contribute to the adiposity phenotype. Interestingly, under conditions of CR, iePPARγKO mice failed to activate their sympathetic nervous system (SNS) and increase CR-specific locomotor activity. These KO mice also manifested a defective control of their body temperature, which was overly reduced. Furthermore, the white adipose tissue of iePPARγKO CR mice showed lower levels of both hormone-sensitive lipase, and its phosphorylated form. This would result from impaired SNS signalling and possibly cause reduced lipolysis. We conclude that intestinal epithelium PPARγ plays an essential role in increasing SNS activity under CR conditions, thereby contributing to energy mobilization during metabolically stressful episodes

Long-term endurance and safety of elosulfase alfa enzyme replacement therapy in patients with Morquio A syndrome

Long-term efficacy and safety of elosulfase alfa enzyme replacement therapy were evaluated in Morquio A patients over 96weeks (reaching 120weeks in total from pre-treatment baseline) in an open-label, multi-center, phase III extension study. During this extension of a 24-week placebo-controlled phase III study, all patients initially received 2.0mg/kg elosulfase alfa either weekly or every other week, prior to establishment of 2.0mg/kg/week as the recommended dose, at which point all patients received weekly treatment. Efficacy measures were compared to baseline of the initial 24-week study, enabling analyses of changes over 120weeks. In addition to performing analyses for the entire intent-to-treat (ITT) population (N=173), analyses were also performed for a modified per-protocol (MPP) population (N=124), which excluded patients who had orthopedic surgery during the extension study or were non-compliant with the study protocol (as determined by ≥20% missed infusions). Six-minute walk test (6MWT) was the primary efficacy measure; three-minute stair climb test (3MSCT) and normalized urine keratan sulfate (uKS) were secondary efficacy measures. Mean (SE) change from baseline to Week 120 in 6MWT distance was 32.0 (11.3)m and 39.9 (10.1)m for patients receiving elosulfase alfa at 2.0mg/kg/week throughout the study (N=56) and 15.1 (7.1)m and 31.7 (6.8)m in all patients combined, regardless of dosing regimen, for the ITT and MPP populations, respectively. Further analyses revealed that durability of 6MWT improvements was not impacted by baseline 6MWT distance, use of a walking aid, or age. Mean (SE) change at Week 120 in the 3MSCT was 5.5 (1.9) and 6.7 (2.0)stairs/min for patients receiving elosulfase alfa at 2.0mg/kg/week throughout the study and 4.3 (1.2) and 6.8 (1.3)stairs/min in all patients combined, regardless of dosing regimen, for the ITT and MPP populations, respectively Across all patients, mean (SE) change at Week 120 in normalized uKS was -59.4 (1.8)% and -62.3 (1.8)% in the ITT and MPP populations, respectively. In the absence of a placebo group, significance of the sustained improvements could not be evaluated directly. However, to provide context for interpretation of results, comparisons were performed with untreated patients from a Morquio A natural history study. In contrast to the results of the extension study, the untreated patients experienced constant uKS levels and a gradual decline in endurance test results over a similar period of time. Differences from the untreated natural history study patients were significant for 6MWT, 3MSCT, and uKS outcomes for the cohort of patients receiving optimal dosing throughout the study and for all cohorts pooled together, for both ITT and MPP populations (P<0.05). Safety findings were consistent with those of the initial 24-week study, with no new safety signals identified

Recommendations for initiation and cessation of enzyme replacement therapy in patients with Fabry disease: the European Fabry Working Group consensus document.

To access publisher's full text version of this article, please click on the hyperlink in Additional Links field or click on the hyperlink at the top of the page marked Files. This article is open access.Fabry disease (FD) is a lysosomal storage disorder resulting in progressive nervous system, kidney and heart disease. Enzyme replacement therapy (ERT) may halt or attenuate disease progression. Since administration is burdensome and expensive, appropriate use is mandatory. We aimed to define European consensus recommendations for the initiation and cessation of ERT in patients with FD.A Delphi procedure was conducted with an online survey (n = 28) and a meeting (n = 15). Patient organization representatives were present at the meeting to give their views. Recommendations were accepted with ≥75% agreement and no disagreement.For classically affected males, consensus was achieved that ERT is recommended as soon as there are early clinical signs of kidney, heart or brain involvement, but may be considered in patients of ≥16 years in the absence of clinical signs or symptoms of organ involvement. Classically affected females and males with non-classical FD should be treated as soon as there are early clinical signs of kidney, heart or brain involvement, while treatment may be considered in females with non-classical FD with early clinical signs that are considered to be due to FD. Consensus was achieved that treatment should not be withheld from patients with severe renal insufficiency (GFR < 45 ml/min/1.73 m(2)) and from those on dialysis or with cognitive decline, but carefully considered on an individual basis. Stopping ERT may be considered in patients with end stage FD or other co-morbidities, leading to a life expectancy of <1 year. In those with cognitive decline of any cause, or lack of response for 1 year when the sole indication for ERT is neuropathic pain, stopping ERT may be considered. Also, in patients with end stage renal disease, without an option for renal transplantation, in combination with advanced heart failure (NYHA class IV), cessation of ERT should be considered. ERT in patients who are non-compliant or fail to attend regularly at visits should be stopped.The recommendations can be used as a benchmark for initiation and cessation of ERT, although final decisions should be made on an individual basis. Future collaborative efforts are needed for optimization of these recommendations.Ministry of Health (ZonMw

Delphi consensus on the current clinical and therapeutic knowledge on Anderson-Fabry disease

BACKGROUND: Management of Anderson-Fabry disease (AFD) is contentious, particularly regarding enzyme replacement therapy (ERT). We report results of a Delphi consensus panel on AFD management. METHODS: A survey to gauge consensus among AFD experts was distributed online and responses were analysed. Statements on: 1) diagnosis; 2) when starting ERT; 3) management of ERT infusion and adverse reactions; and 4) follow-up/monitoring response to therapy and progression of disease were included. Responses without consensus were discussed with an enlarged panel and modified to reach consensus. RESULTS: 15 experts responded to the survey. After plenary discussion among the enlarged panel, consensus was reached on most statements. Key points were the use of a target organ biopsy to show Gb3 deposits in symptomatic women with negative molecular analysis, the need for ERT in symptomatic women and in all patients with persistent signs and symptoms±organ damage. It was agreed to assess vital signs before ERT administration and use a 0.2μL filter on infusion to reduce the risk of adverse reactions, that serum should be drawn prior to the first infusion for anti-agalsidase antibody analysis to have a baseline value if a subsequent adverse reaction appears, and that pre-medication is required in those with prior infusion reactions. Holter ECG monitoring, cardiac and brain MRI, renal parameters, and abdominal ultrasound were considered important for the assessment of disease progression and response at ERT. CONCLUSIONS: This consensus supplies guidance to healthcare providers on best practice in the management of patients with AFD and indicates a need for more guidanc

Investigating the use of a hybrid plasmonic–photonic nanoresonator for optical trapping using finite-difference time-domain method

We investigate the use of a hybrid nanoresonator comprising a photonic crystal (PhC) cavity coupled to a plasmonic bowtie nanoantenna (BNA) for the optical trapping of nanoparticles in water. Using finite difference time-domain simulations, we show that this structure can confine light to an extremely small volume of ~30,000 nm3 (~30 zl) in the BNA gap whilst maintaining a high quality factor (5400–7700). The optical intensity inside the BNA gap is enhanced by a factor larger than 40 compared to when the BNA is not present above the PhC cavity. Such a device has potential applications in optical manipulation, creating high precision optical traps with an intensity gradient over a distance much smaller than the diffraction limit, potentially allowing objects to be confined to much smaller volumes and making it ideal for optical trapping of Rayleigh particles (particles much smaller than the wavelength of light)