Inverse problems for pp-Laplace type equations under monotonicity assumptions

We consider inverse problems for $p$-Laplace type equations under monotonicity assumptions. In two dimensions, we show that any two conductivities satisfying $\sigma_1 \geq \sigma_2$ and having the same nonlinear Dirichlet-to-Neumann map must be identical. The proof is based on a monotonicity inequality and the unique continuation principle for $p$-Laplace type equations. In higher dimensions, where unique continuation is not known, we obtain a similar result for conductivities close to constant.Comment: 17 page

Pion-nucleon Sigma Term in the Global Color Model of QCD

We study the pion-nucleon sigma term in vacuum and in nuclear matter in the framework of global color model of QCD. With the effective gluon propagator being taken as the $\delta$-function in momentum space of Munczek-Nomirovsky model, we estimate that the sigma term at chiral limit in the vacuum is 9/2 times the current quark mass and it decreases with the nuclear matter density. With the presently obtained in-medium pion-nucleon sigma term, we study the in-medium chiral quark condensate and obtain a reasonable variation behavior against the nuclear matter density.Comment: 17 pages, 3 figure

Intrinsic geometry and analysis of Finsler structures

In this short note, we prove that if F is a weak upper semicontinuous admissible Finsler structure on a domain in Rn,n≥2Rn,n≥2\mathbb {R}^n, n\ge 2, then the intrinsic distance and differential structures coincide