A singular Monge-Ampère equation on unbounded domains
In this paper, we study the Dirichlet problem for a singular Monge-Ampere type equation on unbounded domains. For a few special kinds of unbounded convex domains,we find the explicit formulas of the solutions to the problem. For general unbounded convex domain $\Om$, we prove the existence for solutions to the problem in the space$C^{\infty}(\Om)\cap~C~(\overline{\Om})$. We also obtain the local $C^{\frac{1}{2}}$-estimate up to the $\partial~\Omega$ and the estimate for the lower bound of the solutions.
We describe preliminary results from an effort to quantify the uncertainties in parton distribution functions and the resulting uncertainties in predicted physical quantities. The production cross section of the $W$ boson is given as a first example. Constraints due to the full data sets of the CTEQ global analysis are used in this study. Two complementary approaches, based on the Hessian and the Lagrange multiplier method respectively, are outlined. We discuss issues on obtaining meaningful uncertainty estimates that include the effect of correlated experimental systematic uncertainties and illustrate them with detailed calculations using one set of precision DIS data.