In this paper we consider the Monge-Ampère equation det(D2u) = f(x) in a convex domain Ω ⊂ IRn subject to the Dirichlet boundary condition u = φ on ∂Ω. We prove that if ∂Ω and φ are C3 smooth, then the solution u ∈ C2+α(Ω). We also give examples to show that if ∂Ω or φ is only C2,1 smooth, the solution may fail to be C2 smooth near the boundary.

We construct a special plurisubharmonic defining function for a smoothly bounded strictly pseudoconvex domain so that the determinant of the complex Hessian vanishes to high order on the boundary. This construction, coupled with regularity of solutions of complex Monge-Ampére equation and the reflection principle, enables us to give a new proof of the Fefferman mapping theorem.

The use of a systemic approach allows us to analyse the interrelationship between the vegetation dynamic and the agricultural practices through three biological indicators which relate to one hundred paddocks in six cattle farms. Concerning the vegetation dynamics, it seems that some management practices lead to a nonreversable degradation stage. As regards the forage system, the measure of swa...

This article is focused on historical agricultural landscapes in Slovakia, which have been preserved and have irreplaceable ecological, cultural and historical value. Historical structures of agricultural landscapes (HSAL) are a type of cultural landscape that contains, within a geographic area, both natural and man-made features that typify connected activities, and a cultural expression refle...

This paper addresses the question of how the vertical structure of a product line relates to brand equity. Does the presence of “premium” or high-quality products in a product line enhance brand equity? Conversely, does the presence of “economy” or low-quality products in a product line diminish brand equity? Economists and marketing researchers refer to variation in quality levels of products ...

most of the analyses and modeling concerning the mountain physical and human environmental changes have been based on theoretical speculation rather than scientific field observations. lack of standard observations and measurements in scattered and case specific monitoring programs offer only partially useful results for planning and management. all propositions and conclusions are hence mingle...

Last month the Australian Alps were awarded National Heritage status in recognition of the outstanding natural and cultural significance of Australia’s most spectacular mountain range. The heritage listing applies to a group of national parks that encompass the High Country in Victoria, the Snowy Mountains in New South Wales, and the Brindabella Ranges in the Australian Capital Territory and to...

theory? What is its legacy today in biology? Quite a few mathematical fads have burst onto the popular press, promising great new insights into biology: information theory, catastrophe theory, chaos theory, and most recently complexity theory, to name just a few. All were quite useful in their founding fields (except complexity, which has proven slippery to even define), but all failed to live ...

This paper is concerned with the existence of homoclinic solutions for a class of second order p-Laplacian systems with impulsive effects. A new result is obtained under more relaxed conditions by using the mountain pass theorem, a weak convergence argument, and a weak version of Lieb’s lemma. MSC: 34C37; 35A15; 37J45; 47J30