Nonlinear differential equations under perturbations of the domain

En esta tesis estudiamos el comportamiento de ecuaciones diferenciales no lineales bajo perturbacionesdel dominio. En este sentido, extendemos el teorema de V. Sverák presentando condiciones capacitariassuficientes sobre la convergencia de dominios para asegurar la continuidad de las soluciones delp(x)−laplaciano y el p−laplaciano fraccionario y luego analizamos la derivada de forma de unfuncional de costo que surge en el trabajo con restauracion de imágenes.In this thesis we study the behaviour of nonlinear differential equations under perturbations ofthe domain. In this sense, we present extensions of V. Sverak’s theorem giving capacitary conditionson the convergence of the domains in order to obtain the continuity of the solutions for thep(x)−laplacian and the fractional p−laplacian and then we analize the shape derivative of a costfunctional that appears naturally in image restoration.Fil: Baroncini, Carla Antonella. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Continuity results with respect to domain perturbation for the fractional p-Laplacian

In this paper, we give sufficient conditions on the approximating domains in order to obtain the continuity of solutions for the fractional p-Laplacian. These conditions are given in terms of the fractional capacity of the approximating domains.Fil: Baroncini, Carla Antonella. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Fernandez Bonder, Julian. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Spedaletti, Juan Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentin

COVID-19 Severity in Multiple Sclerosis: Putting Data Into Context

Background and objectives: It is unclear how multiple sclerosis (MS) affects the severity of COVID-19. The aim of this study is to compare COVID-19-related outcomes collected in an Italian cohort of patients with MS with the outcomes expected in the age- and sex-matched Italian population. Methods: Hospitalization, intensive care unit (ICU) admission, and death after COVID-19 diagnosis of 1,362 patients with MS were compared with the age- and sex-matched Italian population in a retrospective observational case-cohort study with population-based control. The observed vs the expected events were compared in the whole MS cohort and in different subgroups (higher risk: Expanded Disability Status Scale [EDSS] score > 3 or at least 1 comorbidity, lower risk: EDSS score ≤ 3 and no comorbidities) by the χ2 test, and the risk excess was quantified by risk ratios (RRs). Results: The risk of severe events was about twice the risk in the age- and sex-matched Italian population: RR = 2.12 for hospitalization (p < 0.001), RR = 2.19 for ICU admission (p < 0.001), and RR = 2.43 for death (p < 0.001). The excess of risk was confined to the higher-risk group (n = 553). In lower-risk patients (n = 809), the rate of events was close to that of the Italian age- and sex-matched population (RR = 1.12 for hospitalization, RR = 1.52 for ICU admission, and RR = 1.19 for death). In the lower-risk group, an increased hospitalization risk was detected in patients on anti-CD20 (RR = 3.03, p = 0.005), whereas a decrease was detected in patients on interferon (0 observed vs 4 expected events, p = 0.04). Discussion: Overall, the MS cohort had a risk of severe events that is twice the risk than the age- and sex-matched Italian population. This excess of risk is mainly explained by the EDSS score and comorbidities, whereas a residual increase of hospitalization risk was observed in patients on anti-CD20 therapies and a decrease in people on interferon

DMTs and Covid-19 severity in MS: a pooled analysis from Italy and France

We evaluated the effect of DMTs on Covid-19 severity in patients with MS, with a pooled-analysis of two large cohorts from Italy and France. The association of baseline characteristics and DMTs with Covid-19 severity was assessed by multivariate ordinal-logistic models and pooled by a fixed-effect meta-analysis. 1066 patients with MS from Italy and 721 from France were included. In the multivariate model, anti-CD20 therapies were significantly associated (OR = 2.05, 95%CI = 1.39–3.02, p < 0.001) with Covid-19 severity, whereas interferon indicated a decreased risk (OR = 0.42, 95%CI = 0.18–0.99, p = 0.047). This pooled-analysis confirms an increased risk of severe Covid-19 in patients on anti-CD20 therapies and supports the protective role of interferon

Nonlinear differential equations under perturbations of the domain

En esta tesis estudiamos el comportamiento de ecuaciones diferenciales no lineales bajo perturbacionesdel dominio. En este sentido, extendemos el teorema de V. Sverák presentando condiciones capacitariassuficientes sobre la convergencia de dominios para asegurar la continuidad de las soluciones delp(x)−laplaciano y el p−laplaciano fraccionario y luego analizamos la derivada de forma de unfuncional de costo que surge en el trabajo con restauracion de imágenes.In this thesis we study the behaviour of nonlinear differential equations under perturbations ofthe domain. In this sense, we present extensions of V. Sverak’s theorem giving capacitary conditionson the convergence of the domains in order to obtain the continuity of the solutions for thep(x)−laplacian and the fractional p−laplacian and then we analize the shape derivative of a costfunctional that appears naturally in image restoration.Fil: Baroncini, Carla Antonella. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

An extension of a theorem of V. Šverák to variable exponent spaces

In 1993, V. Šverák proved that if a sequence of uniformly bounded domains Ωn ℝ2 such that Ωn → Ω in the sense of the Hausdorff complementary topology, verify that the number of connected components of its complements are bounded, then the solutions of the Dirichlet problem for the Laplacian with source f ∈ L2(ℝ2) converges to the solution of the limit domain with same source. In this paper, we extend Šverák result to variable exponent spaces.Fil: Baroncini, Carla Antonella. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Fernandez Bonder, Julian. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentin

SARS-CoV-2 serology after COVID-19 in multiple sclerosis: An international cohort study

Background: The MuSC-19 project is an Italian cohort study open to international partners that collects data on multiple sclerosis (MS) patients with COVID-19. During the second wave of the pandemic, serological tests became routinely available. Objective: To evaluate the seroprevalence of anti-SARS-CoV-2 antibodies according to the use of disease-modifying therapy (DMT) in a subset of patients included in the MuSC-19 data set who had undergone a serological test. Methods: We evaluated the association between positive serological test results and time elapsed since infection onset, age, sex, Expanded Disability Status Scale score, comorbidities and DMT exposure using a multivariable logistic model. Results: Data were collected from 423 patients (345 from Italy, 61 from Turkey and 17 from Brazil) with a serological test performed during follow-up. Overall, 325 out of 423 tested patients (76.8%) had a positive serological test. At multivariate analysis, therapy with anti-CD20 was significantly associated with a reduced probability of developing antibodies after COVID-19 (odds ratio (OR) = 0.20, p = 0.002). Conclusion: Patients with MS maintain the capacity to develop humoral immune response against SARS-COV-2, although to a lesser extent when treated with anti-CD20 drugs. Overall, our results are reassuring with respect to the possibility to achieve sufficient immunization with vaccination

Signs and symptoms of COVID-19 in patients with multiple sclerosis

Clinical outcomes of multiple sclerosis (MS) patients affected by coronavirus disease 2019 (COVID-19) have been thoroughly investigated, but a further analysis on main signs and symptoms and their risk factors still needs attention. The objective of this study was to group together and describe based on similarity the most common signs and symptoms of COVID-19 in MS patients and identify all factors associated with their manifestation

The effect of air pollution on COVID-19 severity in a sample of patients with multiple sclerosis

Some studies have shown that air pollution, often assessed by thin particulate matter with diameter below 2.5 µg/m3 (PM2.5), may contribute to severe COVID-19 courses, as well as play a role in the onset and evolution of multiple sclerosis (MS). However, the impact of air pollution on COVID-19 has never been explored specifically amongst patients with MS (PwMS). This retrospective observational study aims to explore associations between PM2.5 and COVID-19 severity amongst PwMS