41 research outputs found
Some homogenization and corrector results for nonlinear monotone operators
This paper deals with the limit behaviour of the solutions of quasi-linear
equations of the form \ \ds -\limfunc{div}\left(a\left(x, x/{\varepsilon
_h},Du_h\right)\right)=f_h on with Dirichlet boundary conditions.
The sequence tends to and the map is
periodic in , monotone in and satisfies suitable continuity
conditions. It is proved that weakly in , where is the solution of a homogenized problem \
-\limfunc{div}(b(x,Du))=f on . We also prove some corrector results,
i.e. we find such that in
Management of Hepatitis C Antiviral Therapy Adverse Effects
Hepatitis C is one of the leading causes of liver disease in the United States, affecting more than 4 million individuals. The current treatment regimen involves pegylated interferon in combination with ribavirin. Although antiviral treatment has been associated with a greater than 50% sustained viral response rate, the adverse effects have proven to be detrimental to quality of life and therapy adherence, and consequently lead to lower sustained viral response rates. This article identifies the most frequently described complications associated with pegylated interferon and ribavirin. The active management of these complications is discussed, including both preventive and empiric treatments
Asymptotic behaviour of quasi-linear problems with Neumann boundary conditions on perforated domains
A compactness result for a second-order variational discrete model.
We analyze a nonlinear discrete scheme depending on second-order finite differences. This is the two-dimensional analog of a scheme which in one dimension approximates a free-discontinuity energy proposed by Blake and Zisserman as a higher-order correction of the Mumford and Shah functional. In two dimension we give a compactness result showing that the continuous problem approximating this difference scheme is still defined on special functions with bounded hessian, and we give an upper and a lower bound in terms of the Blake and Zisserman energy. We prove a sharp bound by exhibiting the discrete-to-continuous Γ-limit for a special class of functions, showing the appearance new ‘shear’ terms in the energy, which are a genuinely two-dimensional effect