A stability result for elliptic equations with singular nonlinearity and its applications to homogenization problems

We consider model semilinear elliptic equations of the type $$\begin{cases} - \mathrm{div} (A(x) \nabla u) = f u^{- \lambda}, \quad u > 0 \quad \text{in} \ \Omega, \\ u \in H_{0}^{1}(\Omega), \end{cases}$$ where $\Omega$ is a bounded domain in $\mathbf{R}^{N}$, $N \ge 1$, $A \in L^{\infty}(\Omega)^{N \times N}$ is a coercive matrix, $0 < \lambda \le 1$ and $f$ is a nonnegative function in $L^{1}_{loc}(\Omega)$, or more generally, nonnegative Radon measure on $\Omega$. We discuss $H^{1}$-stability of $u$ under a minimal assumption on $f$. Additionally, we apply the result to homogenization problems

ドリフトをもつ楕円型方程式に対するRieszポテンシャル評価

首都大学東京, 2016-03-25, 博士（理学）, 甲第563号首都大学東

Existence of minimal solutions to quasilinear elliptic equations with several sub-natural growth terms

We study the existence of positive solutions to quasilinear elliptic equations of the type $$-\Delta_{p} u = \sigma u^{q} + \mu \quad \text{in} \ \mathbb{R}^{n},$$ in the sub-natural growth case $0 < q < p - 1$, where $\Delta_{p}u = \nabla \cdot ( |\nabla u|^{p - 2} \nabla u )$ is the $p$-Laplacian with $1 < p < n$, and $\sigma$ and $\mu$ are nonnegative Radon measures on $\mathbb{R}^{n}$. We construct minimal generalized solutions under certain generalized energy conditions on $\sigma$ and $\mu$. To prove this, we give new estimates for interaction between measures. We also construct solutions to equations with several sub-natural growth terms using the same methods.Comment: Published online in Nonlinear Analysi

Extended-criteria donors in liver transplantation Part II: reviewing the impact of extended-criteria donors on the complications and outcomes of liver transplantation

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Extended criteria donors in liver transplantation Part I: reviewing the impact of determining factors

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Is preservation of middle hepatic vein tributaries during right hemi-hepatectomy beneficial for live donor liver transplantation?

Background/Aims: When right hemi-hepatectomy without middle hepatic vein (MHV) is performed in a living donor (LD), MHV tributaries such as V5 and V8 may be preserved during parenchymal transection to preserve liver function and reduce the damage of the graft. However, no study has so far investigated whether this preservation of MHV tributaries during parenchymal transection has impact on live donor operation or graft function. Methodology: Of 52 hepatectomies for right lobe LD, MHV tributaries were preserved during hepatic parenchymal transection in 11 cases, while, in the remaining 41 cases MHV tributaries were sacrificed when those were encountered during hepatic parenchymal transection. Results: There was no significant difference in blood loss, operative time, zenith liver enzyme level in a donor and rate of graft failure in a recipient. Conclusions: It was demonstrated that there was no significant effect of outflow preservation from MHV tributaries on LD hepatectomy for right lobe donation and subsequent liver transplantation

Effect of pre‐transplant sarcopenia on the estimation of standard liver volume in living‐donor liver transplant candidates: risk factor for post‐transplant small‐for‐size syndrome? A retrospective study

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Standardized less invasive living donor hemihepatectomy by the hybrid method through short upper midline incision

Recently, applications of less invasive liver surgery in living donor hepatectomy (LDH) have been reported. The objective of this study was to evaluate the safety and efficacy of a hybrid method with a midline incision for LDH

Long-term culture of rat hepatocytes using human amniotic membrane as a culture substrate

Amniotic membrane is attracting attention as a new material for regenerative medicine. We herein report that the culture of primary rat hepatocytes on human amniotic membrane maintained their morphology and their production of albumin for at least two months. Human amniotic membrane was collected during planned cesarean section and kept frozen until usage. Primary rat hepatocytes were plated on human amniotic membrane. Hepatocytes accumulated as colonies on amniotic membrane, and their rat albumin level was maintained for two months. Their three-dimensional structure on extracellular matrix, which is abundant in amniotic membranes might influence the maintenance of the hepatocyte-specific function

A Predictive Formula for Portal Venous Pressure Prior to Liver Resection Using Directly Measured Values

Purpose: Despite refinements in surgical techniques for liver resection, evaluation of hepatic reserve disparity remains one of the most common problems in liver surgery, especially for hepatic malignancies such as hepatocellular carcinoma (HCC). Portal venous pressure (PVP) is regarded one of the important factors in selecting treatment strategy, although its measurement can be invasive and complex. Methods: To establish a formula for calculating PVP preoperatively, intraoperative directly measured PVP was used in 177 patients with preoperative factors and liver function tests such as age, sex, virus status, platelet count, prothrombin time, albumin, total bilirubin, alanine aminotransferase (ALT), Child?Pugh grade, liver damage defined by the Liver Cancer Study Group of Japan, indocyanine green retention rate at 15 min (ICG-R15), and the aspartate transaminase (AST)-platelet ratio index (APRI). Results: Although 90% of the patients were classified as Child-Pugh A, median direct PVP was 16.5 cm H2O (5.5?37.0) and the percentage of PVP greater than 20 cm H2O was 27.1%, reflecting portal hypertension due to liver damage. After multiple regression analysis, the formula PVP (cmH2O) = EXP[2.606 + 0.01 × (ICG-R15) + 0.015 × APRI] was established from the measured data. Conclusion: Considering its simplicity of use, we have adopted this formula for predicting PVP in determining treatment strategy for HCC and other hepatic malignancies