A Nonlinear Functional on the Dirichlet Space

the effect of functional/notional approach on the proficiency level of efl learners and its evaluation through functional test

in fact, this study focused on the following questions: 1. is there any difference between the effect of functional/notional approach and the structural approaches to language teaching on the proficiency test of efl learners? 2. can a rather innovative language test referred to as "functional test" ge devised so so to measure the proficiency test of efl learners, and thus be as much reliable an...

Dirichlet Duality and the Nonlinear Dirichlet Problem on Riemannian Manifolds

In this paper we study the Dirichlet problem for fully nonlinear secondorder equations on a riemannian manifold. As in our previous paper [HL4] we define equations via closed subsets of the 2-jet bundle where each equation has a natural dual equation. Basic existence and uniqueness theorems are established in a wide variety of settings. However, the emphasis is on starting with a constant coeff...

The Dirichlet space: a survey

6 The multiplier space and other spaces intrinsic to D theory 24 6.1 Multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 6.2 The weakly factored space D D and its dual . . . . . . . . . . . 25 6.3 The Corona Theorem . . . . . . . . . . . . . . . . . . . . . . . . 27 6.3.1 The ∂-equation in the Dirichlet Space . . . . . . . . . . . 28 6.3.2 Corona Theorems and Complete Nev...

The Dirichlet Space on the bi-disc

Dirichlet Duality and the Nonlinear Dirichlet Problem

We study the Dirichlet problem for fully nonlinear, degenerate elliptic equations of the form F.Hessu/ D 0 on a smoothly bounded domain  b Rn. In our approach the equation is replaced by a subset F Sym.Rn/ of the symmetric n nmatrices with @F fF D 0g. We establish the existence and uniqueness of continuous solutions under an explicit geometric “F -convexity” assumption on the boundary @. We a...