We obtain a priori interior Hessian and gradient estimates for special Lagrangian equations with phase larger than a critical value in dimension three. Gradient estimates are also derived for critical and super critical phases in general dimensions.

The horizontal wavenumber spectra of wind and temperature near the tropopause have a steep 23 slope at synoptic scales and a shallower 25/3 slope at mesoscales, with a transition between the two regimes at a wavelength of about 450 km. Here it is demonstrated that a quasigeostrophic model driven by baroclinic instability exhibits such a transition near its upper boundary (analogous to the tropo...

In this paper we give a simple proof for the interior gradient estimate for curvature and Hessian equations. We also derive a Liouville type result for these equations. §0. Introduction The interior gradient estimate for the prescribed mean curvature equation has been extensively studied, see [9] and the references therein. For high order mean curvature equations it has also been obtained in [1...

In this paper, we study diagonally scaled gradient methods for simple-bound constrained optimization in a framework almost identical to that for unconstrained optimization, except that iterates are kept within the interior of the feasible region. We establish a satisfactory global convergence theory for such interior-point gradient methods applied to Lipschitz continuously differentiable functi...

In this paper we are concerned with the application of interior point methods in function space to gradient constrained optimal control problems, governed by partial differential equations. We will derive existence of solutions together with first order optimality conditions. Afterwards we show continuity of the central path, together with convergence rates depending on the interior point param...

A technique for the efficient entrapment of high concentrations of Ca2+ in large unilamellar phospholipid vesicles (LUVs), using the carboxylic acid antibiotic ionophore A23187 (calcimycin) is demonstrated. It is shown that rapid A23187-mediated entrapment of Ca2+, corresponding to essentially 100% sequestration of the extravesicular cation may be achieved for egg yolk phosphatidylcholine LUVs ...