Investigating for interior regularity of viscosity solutions to the fully nonlinear elliptic equation F (x, u,▽u,▽u) = 0, we establish the interior C continuity under the assumptions that F is uniformly elliptic, Hölder continuous and satisfies the natural structure conditions of fractional order, but without the concavity assumption of F . These assumptions are weaker and the result is stronge...

In this paper we study fully nonlinear obstacle type problems in Hilbert spaces. We introduce the notion of Q-elliptic equation and prove existence, uniqueness, and regularity of viscosity solutions of Q-elliptic obstacle problems. In particular we show that solutions of concave problems with semiconvex obstacles are in the space W 2,∞ Q .

We derive a priori interior Hessian estimates for special Lagrangian equations when the potential is convex. When the phase is very large, we show that continuous viscosity solutions are smooth in the interior of the domain. c 2008 Wiley Periodicals, Inc.

Inspired by the penalization of the domain approach of Lions & Sznitman, we give a sense to Neumann and oblique derivatives boundary value problems for nonlocal, possibly degenerate elliptic equations. Two different cases are considered: (i) homogeneous Neumann boundary conditions in convex, possibly non-smooth and unbounded domains, and (ii) general oblique derivatives boundary conditions in s...

Biodiesel produced from vegetable oils, animal fats and algae oil is a renewable, environmentally friendly and clean alternative fuel that reduces pollutants and greenhouse gas emissions in marine applications. This study investigates the influence of biodiesel blend on the characteristics of residual and distillate marine fuels. Adequate correlation equations are applied to calculate the fuel ...

We consider the generalized evolution of compact level sets by functions of their normal vectors and second fundamental forms on a Riemannian manifold M . The level sets of a function u : M → R evolve in such a way whenever u solves an equation ut + F (Du,Du) = 0, for some real function F satisfying a geometric condition. We show existence and uniqueness of viscosity solutions to this equation ...

The paper proves a new uniqueness result for viscosity solutions of the Dirichlet problem for Hamilton-Jacobi equations of the form H(x; u; D x 0 u) = 0 in ; u = g on @; where is an open subset or R n and D x 0 u is the partial gradient of the scalar function u with respect to the rst n 0 variables (n 0 n). The main theorem states that there is a viscosity solution of the equation which is uniq...

residual gas saturation is one of the most important parameter in determining recovery factor of water-drive gas reservoir. visual observation of processes occurring at the pore level in micromodels can give an insight to fluid displacements at the larger scale and also help the interpretation of production performance at reservoir scale. in this study experimental tests in a glass micromodel w...

BACKGROUND AND OBJECTIVES Increased vascular wall shear stress by elevated plasma viscosity significantly enhances the endothelial nitric oxide synthase (eNOS) activity during an acute isovolemic hemodilution. Also the modulation of plasma viscosity has effects on the cardiac function that were revealed if a left ventricular (LV) pressure-volume (PV) measurement was used. The aim of this study ...

In this paper, a central discontinuous Galerkin method is proposed to solve for the viscosity solutions of Hamilton-Jacobi equations. Central discontinuous Galerkin methods were originally introduced for hyperbolic conservation laws. They combine the central scheme and the discontinuous Galerkin method and therefore carry many features of both methods. Since Hamilton-Jacobi equations in general...