Homogenization of a parabolic Dirichlet problem by a method of Dahlberg

Consider the linear parabolic operator in divergence form $$\mathcal{H} u =\partial_t u(X,t)-\text{div}(A(X)\nabla u(X,t)).$$ We employ a method of Dahlberg to show that the Dirichlet problem for $\mathcal{H}$ in the upper half plane is well-posed for boundary data in $L^p$, for any elliptic matrix of coefficients $A$ which is periodic and satisfies a Dini-type condition. This result allows us to treat a homogenization problem for the equation $\partial_t u_\varepsilon(X,t)-\text{div}(A(X/\varepsilon)\nabla u_\varepsilon(X,t))$ in Lipschitz domains with $L^p$-boundary data.Comment: 21 page

Homogenization of a parabolic Dirichlet problem by a method of Dahlberg

Consider the linear parabolic operator in divergence form Hu := ∂tu(X, t) − div(A(X)∇u(X, t)). We employ a method of Dahlberg to show that the Dirichlet problem for H in the upper half plane is well-posed for boundary data in Lp, for any elliptic matrix of coefficients A which is periodic and satisfies a Dini-type condition. This result allows us to treat a homogenization problem for the equation ∂tuε(X, t) − div(A(X/ε)∇uε(X, t)) in Lipschitz domains with Lp-boundary data.Consider the linear parabolic operator in divergence form Hu := ∂tu(X, t) − div(A(X)∇u(X, t)). We employ a method of Dahlberg to show that the Dirichlet problem for H in the upper half plane is well-posed for boundary data in Lp, for any elliptic matrix of coefficients A which is periodic and satisfies a Dini-type condition. This result allows us to treat a homogenization problem for the equation ∂tuε(X, t) − div(A(X/ε)∇uε(X, t)) in Lipschitz domains with Lp-boundary data

The Swedish Spine Register: development, design and utility

The Swedish Spine Register enables monitoring of surgical activities focusing on changes in trends over time, techniques utilized and outcome, when implemented in general clinical practice. Basic requirements for a prosperous register are unity within the profession, mainly patient-based documentation and a well functioning support system. This presentation focuses on the development and design of the register protocol, problems encountered and solutions found underway. Various examples on how the results can be presented and utilized are given as well as validation. Register data demonstrate significant gender differences in lumbar disc herniation surgery with females having more pain, lower quality of life and more pronounced disability preoperatively while improvement after surgery is similar between genders. Quality of life after surgery for degenerative disorders is significantly improved for disc herniation, stenosis, spondylolisthesis and disc degenerative disorders. Over the last 10 years, surgical treatment for spinal stenosis has increased gradually while disc herniation surgery decreases regarding yearly number of procedures. An added function to the register enables more complex prospective clinical studies to include register data together with data suitable for the individual study. A common core set of demographic, surgical and outcome parameters would enable comparisons of clinical studies within and between nations

Comparing estimated cost per patient for dementia care: Two municipalities and Swedish national population data

Abstract Aim: To evaluate a collaborative dementia program for its influence on cost and in which dementia care specialists and primary care centres collaborate with the municipality and, thereby, effect direct cost of dementia care. Methods: The cost of illness (COI) study investigated the cost of dementia care to the municipality, specifically on the Municipality of Kalmar. Municipal costs in the Municipality of Älvsjö and national cost figures for Sweden were used as comparisons. The major costs related to dementia care, such as the cost of home care, day-care centers, and nursing home placement were extracted from municipality records. Results: The yearly municipal cost per person with dementia in Kalmar ranged from 14,206 C to 26,334 C (17,684 USD to 32,780 USD) as compared to Älvsjö 10,610 C to 30,464 C (13,207 USD to 37,921 USD), and Swedish national figures showing costs from 23,600 C to 36,459 C (29,378 USD to 45,384 USD), per patient, annual cost. In Kalmar, 60% of the patients with dementia received help from the municipality as compared to 69% in Älvsjö. Conclusions: Implementation of such a dementia program is a recommendation that would not increase the cost for dementia care in the Municipality of Kalmar

Correlation between disability and MRI findings in lumbar spinal stenosis: A prospective study of 109 patients operated on by decompression

Background and purpose MRI is the modality of choice when diagnosing spinal stenosis but it also shows that stenosis is prevalent in asymptomatic subjects over 60. The relationship between preoperative health-related quality of life, functional status, leg and back pain, and the objectively measured dural sac area in single and multilevel stenosis is unknown. We assessed this relationship in a prospective study. Patients and methods The cohort included 109 consecutive patients with central spinal stenosis operated on with decompressive laminectomy or laminotomy. Preoperatively, all patients completed the questionnaires for EQ-5D, SF-36, Oswestry disability index (ODI), estimated walking distance and leg and back pain (VAS). The cross-sectional area of the dural sac was measured at relevant disc levels in mm(2), and spondylolisthesis was measured in mm. For comparison, the area of the most narrow level, the number of levels with dural sac area < 70 mm(2), and spondylolisthesis were studied. Results Before surgery, patients with central spinal stenosis had low HRLQoL and functional status, and high pain levels. Patients with multilevel stenosis had better general health (p = 0.04) and less leg and back pain despite having smaller dural sac area than patients with single-level stenosis. There was a poor correlation between walking distance, ODI, the SF-36, EQ-5D, and leg and back pain levels on the one hand and dural sac area on the other. Women more often had multilevel spinal stenosis (p = 0.05) and spondylolisthesis (p < 0.001). Spondylolisthetic patients more often had small dural sac area (p = 0.04) and multilevel stenosis (p = 0.06). Interpretation Our findings indicate that HRQoL, function, and pain measured preoperatively correlate with morphological changes on MRI to a limited extent

Application of uniform distribution to homogenization of a thin obstacle problem with p-Laplacian

In this paper we study the homogenization of p-Laplacian with thin obstacle in a perforated domain. The obstacle is defined on the intersection between a hyperplane and a periodic perforation. We construct the family of correctors for this problem and show that the solutions for the epsilon-problem converge to a solution of a minimization problem of similar form but with an extra term involving the mean capacity of the obstacle. The novelty of our approach is based on the employment of quasi-uniform convergence. As an application we obtain Poincare's inequality for perforated domains.QC 20140919. Updated from accepted to published.</p