An optimal mass transport approach for limits of eigenvalue problems for the fractional pp-Laplacian

We find interpretation using optimal mass transport theory for eigenvalue problems obtained as limits of the eigenvalue problems for the fractional $p-$Laplacian operators as $p\to +\infty$. We deal both with Dirichlet and Neumann boundary conditions.Comment: 20 page

The dependence of the first eigenvalue of the infinity Laplacian with respect to the domain

In this paper we study the dependence of the first eigenvalue of the infinity Laplace with respect to the domain. We prove that this first eigenvalue is continuous under some weak convergence conditions which are fulfilled when a sequence of domains converges in Hausdorff distance. Moreover, it is Lipschitz continuous but not differentiable when we consider deformations obtained via a vector field. Our results are illustrated with simple examples.Partially supported by MEC MTM2010-18128 (Spain)

Estrogen regulation of apoptosis: how can one hormone stimulate and inhibit?

The link between estrogen and the development and proliferation of breast cancer is well documented. Estrogen stimulates growth and inhibits apoptosis through estrogen receptor-mediated mechanisms in many cell types. Interestingly, there is strong evidence that estrogen induces apoptosis in breast cancer and other cell types. Forty years ago, before the development of tamoxifen, high-dose estrogen was used to induce tumor regression of hormone-dependent breast cancer in post-menopausal women. While the mechanisms by which estrogen induces apoptosis were not completely known, recent evidence from our laboratory and others demonstrates the involvement of the extrinsic (Fas/FasL) and the intrinsic (mitochondria) pathways in this process. We discuss the different apoptotic signaling pathways involved in E2 (17β-estradiol)-induced apoptosis, including the intrinsic and extrinsic apoptosis pathways, the NF-κB (nuclear factor-kappa-B)-mediated survival pathway as well as the PI3K (phosphoinositide 3-kinase)/Akt signaling pathway. Breast cancer cells can also be sensitized to estrogen-induced apoptosis through suppression of glutathione by BSO (L-buthionine sulfoximine). This finding has implications for the control of breast cancer with low-dose estrogen and other targeted therapeutic drugs