Perturbed Obstacle Problems in Lipschitz Domains: Linear Stability and Non-degeneracy in Measure

We consider the classical obstacle problem on bounded, connected Lipschitz domains $D \subset \mathbb{R}^n$. We derive quantitative bounds on the changes to contact sets under general perturbations to both the right hand side and the boundary data for obstacle problems. In particular, we show that the Lebesgue measure of the symmetric difference between two contact sets is linearly comparable to the $L^1$-norm of perturbations in the data.Comment: 9 page

Perturbed Obstacle Problems in Lipschitz Domains: Linear Stability and Nondegeneracy in Measure

We consider the classical obstacle problem on bounded, connected Lipschitz domains D⊂Rn. We derive quantitative bounds on the changes to contact sets under general perturbations to both the right-hand side and the boundary data for obstacle problems. In particular, we show that the Lebesgue measure of the symmetric difference between two contact sets is linearly comparable to the L1-norm of perturbations in the data

Mean Value Theorems for Riemannian Manifolds Via the Obstacle Problem

We develop some of the basic theory for the obstacle problem on Riemannian manifolds, and we use it to establish a mean value theorem. Our mean value theorem works for a very wide class of Riemannian manifolds and has no weights at all within the integral

MET Y1253D-activating point mutation and development of distant metastasis in advanced head and neck cancers

We investigated if the MET-activating point mutation Y1253D influences clinical outcomes in patients with advanced squamous cell carcinoma of the head and neck (HNSCC). The study population consisted of 152 HNSCC patients treated by hyperfractionated radiotherapy alone or concomitant with chemotherapy between September 1994 and July 2000. Tumors were screened for the presence of the MET-activating point mutation Y1253D. Seventy-eight patients (51%) received radiotherapy alone, 74 patients (49%) underwent radiotherapy concomitant with chemotherapy. Median patient age was 54years and median follow-up was 5.5years. Distant metastasis-free survival, local relapse-free survival and overall survival were compared with MET Y1253D status. During follow-up, 29 (19%) patients developed distant metastasis. MET Y1253D was detected in tumors of 21 out of 152 patients (14%). Distant metastasis-free survival (P=0.008) was associated with MET Y1253D. In a multivariate Cox regression model, adjusted for T-category, only presence of MET Y1253D was associated with decreased distant metastasis-free survival: hazard ratio=2.5 (95% confidence interval: 1.1, 5.8). The observed association between MET Y1253D-activating point mutation and decreased distant metastasis-free survival in advanced HNSCC suggests that MET may be a potential target for specific treatment intervention