The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking

This study looked into the various types of user- education offered in Covenant University. These include library orientation, teaching of use of library and study skills, basic bibliographic instructions etc. The research revealed that the highest impact of user education on students is equipping them with good search skills as indicated by 93.9 % respondents, acquainting them with available resources and their format as represented by 82.6 % and exposing them to library rules and regulations among others. The major challenges hindering students from maximizing user education is that of scheduling library orientation too close to resumption as portrayed by 711 (90.8%) respondents and large number of student participants, resulting in noise. The study recommends that the orientation be scheduled after conclusion of admissions so that all students will benefit from it. More periods should be allocated to the teaching of use of library and study skills as well as that of orientation. The study concludes by encouraging Covenant University library to keep building search skills in its new patrons while making adjustments where necessary. It also encourages other university libraries lacking in this regard to follow suit.

This paper treats degenerate parabolic equations of second order (1.1) u t + F{Vu, V 2 w) = 0

We introduce the notion of a "good" solution of a fully nonlinear uniformly elliptic equation. It is proven that "good" solutions are equivalent to L p -viscosity solutions of such equations. The main contribution of the paper is an explicit construction of elliptic equations

We consider the use of Lagrange manifolds to construct viscosity solutions of first order Hamiltonian-Jacobi equations. Recent work of several authors is indicated in which the essential underlying structure consists of a Lagrange manifold on which 1) the desired Hamiltonian function vanishes

Advisor: Prof. Italo Capuzzo DolcettaIf you have a problem you cannot solve, change it into one that you can solve. In other words, if you aren’t near the one you love, love the one you are near. 6 Contents. 2 Viscosity solutions and metric Hopf-Lax formula. 89 2.1 An introduction to the viscosity

. We prove that the explicit formula [2] for viscosity solutions of Hamilton -Jacobi equation @u=@t+H(u;r xu) = 0 in (0; +1) \Theta lR n with u(0; x) = oe(x) is still valid while the initial data oe(x) is continuous in lR n (not necessarily Lipschitz continuous and bounded in lR n

This research report presents an approach to the shape from shading problem which is based upon the notion of viscosity solutions to the shading partial differential equation, in e ect a Hamilton-Jacobi equation. The power of this approach is twofolds: 1) it allows nonsmooth, i.e. nondi erentiable

Abstract. We consider the Dirichlet problem for Hamilton-Jacobi equations and prove existence, uniqueness and continuous dependence on boundary data of Lipschitz continuous maximal viscosity solutions. 1.

In this paper we study Hölder regularity for the first and second derivatives of continuous viscosity solutions of fully nonlinear equations of the form (1.1) F(D 2 u) = 0. It is well known that viscosity solutions of (1.1) are C 1,α for some 0 < α < 1, and