Weighted a priori estimates for the Poisson equation [PDF]
Indiana University Mathematics Journal, 2008 and let u be a solution of the classical Poisson problem in Ω; i.e., -Δu = f in Ω, u = 0 on ∂Ω, where f ∈ L ρ ω (Ω) and ω is a weight in Ap. The main goal of this paper is to prove the following a priori estimate ∥u∥W 2,p ω (Ω)≤C∥f∥L p ω (Ω), and to give some applications for weights given by powers of the distance to the boundary.
Durán, Ricardo Guillermo +2 more
openaire +3 more sources
Copy Number Variants and Their Association With Intracerebral Hemorrhage Risk: A Case–Control Study
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Introduction Intracerebral Hemorrhage (ICH) is a leading cause of morbidity and mortality worldwide and lacks effective therapeutic interventions. Despite previous studies, the genetic underpinnings of ICH remain poorly understood. We sought to investigate the role of copy number variants (CNVs) in ICH pathophysiology to identify novel ...
Savvina Prapiadou +12 more
wiley +1 more source
A priori estimates for anti-symmetric solutions to a fractional Laplacian equation in a bounded domain [PDF]
, 2023 Chenkai Liu, Shaodong Wang, Ran Zhuo
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Maximal Graphs and Spacelike Mean Curvature Flows in Semi-Euclidean Spaces [PDF]
, 2011 Two main results are proved. The first is for the maximal graph system in semi-Euclidean spaces. Existence of smooth solutions to the Dirichlet problem is proved, under certain assumptions on the boundary data.
THORPE, BENJAMIN,STUART
core
The Surrogate Matrix Methodology: A Priori Error Estimation [PDF]
SIAM Journal on Scientific Computing, 2019 We give the first mathematically rigorous analysis of an emerging approach to finite element analysis (see, e.g., Bauer et al. [Appl. Numer. Math., 2017]), which we hereby refer to as the surrogate matrix methodology. This methodology is based on the piece-wise smooth approximation of the matrices involved in a standard finite element discretization ...
Drzisga, Daniel +2 more
openaire +4 more sources
Hospital Readmission After Traumatic Brain Injury Hospitalization in Community‐Dwelling Older Adults
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective To examine the risk of hospital readmission after an index hospitalization for TBI in older adults. Methods Using data from the Atherosclerosis Risk in Communities (ARIC) study, we used propensity score matching of individuals with an index TBI‐related hospitalization to individuals with (1) non‐TBI hospitalizations (primary analysis)
Rachel Thomas +7 more
wiley +1 more source
Positive solutions for elliptic problems with critical indefinite nonlinearity in bounded domains
Electronic Journal of Differential Equations, 2007 In this paper, we study the semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely $$ - Delta u =lambda u + h (x) u^{(n+2)/(n-2)} $$ in a smooth open bounded domain $Omegasubseteq mathbb{R}^n$, $n > 4 $ with ...
Jacques Giacomoni +2 more
doaj
Existence of global solutions to chemotaxis fluid system with logistic source
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We establish the existence of global solutions and $L^q$ time-decay of a three dimensional chemotaxis system with chemoattractant and repellent. We show the existence of global solutions by the energy method.
Harumi Hattori, Aesha Lagha
doaj +1 more source
Admissible solutions to augmented nonsymmetric $k$-Hessian type equations II. A priori estimates and the Dirichlet problem [PDF]
, 2021 Bằng Trần Văn +3 more
openalex +1 more source
Lessons Learned From a Delayed‐Start Trial of Modafinil for Freezing of Gait in Parkinson's Disease
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Freezing of gait (FOG) in people with Parkinson's disease (PwPD) is debilitating and has limited treatments. Modafinil modulates beta/gamma band activity in the pedunculopontine nucleus (PPN), like PPN deep brain stimulation. We therefore tested the hypothesis that Modafinil would improve FOG in PwPD.
Tuhin Virmani +8 more
wiley +1 more source