Some recent results on singular p-Laplacian equations

A short account of some recent existence, multiplicity, and uniqueness results for singular p-Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions. An extensive bibliography is also provided

Existence of two solutions for singular φ-Laplacian problems

Existence of two solutions to a parametric singular quasi-linear elliptic problem is proved. The equation is driven by the Φ-Laplacian operator, and the reaction term can be nonmonotone. The main tools employed are the local minimum theorem and the Mountain pass theorem, together with the truncation technique. Global C^(1,τ) regularity of solutions is also investigated, chiefly via a priori estimates and perturbation techniques

Mast cells boost myeloid-derived suppressor cell activity and contribute to the development of tumor-favoring microenvironment.

Inflammation plays crucial roles at different stages of tumor development and may lead to the failure of immune surveillance and immunotherapy. Myeloid-derived suppressor cells (MDSC) are one of the major components of the immune-suppressive network that favors tumor growth, and their interaction with mast cells is emerging as critical for the outcome of the tumor-associated immune response. Herein, we showed the occurrence of cell-to-cell interactions between MDSCs and mast cells in the mucosa of patients with colon carcinoma and in the colon and spleen of tumor-bearing mice. Furthermore, we demonstrated that the CT-26 colon cancer cells induced the accumulation of CD11b(+)Gr1(+) immature MDSCs and the recruitment of protumoral mast cells at the tumor site. Using ex vivo analyses, we showed that mast cells have the ability to increase the suppressive properties of spleen-derived monocytic MDSCs, through a mechanism involving IFN\u3b3 and nitric oxide production. In addition, we demonstrated that the CD40:CD40L cross-talk between the two cell populations is responsible for the instauration of a proinflammatory microenvironment and for the increase in the production of mediators that can further support MDSC mobilization and tumor growth. In light of these results, interfering with the MDSC:mast cell axis could be a promising approach to abrogate MDSC-related immune suppression and to improve the antitumor immune response. Cancer Immunol Res; 3(1); 85-95. \ua92014 AACR