Mathematical Analysis and Applications

Investigations involving the theory and applications of mathematical analytic tools and techniques are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. In this Special Issue, we invite and welcome review, expository and original research articles dealing with the recent advances in mathematical analysis and its multidisciplinary applications

Mathematical models of martensitic microstructure

Martensitic microstructures are studied using variational models based on nonlinear elasticity. Some relevant mathematical tools from nonlinear analysis are described, and applications given to austenite-martensite interfaces and related topics

Finite Element Analysis: Mathematical Theory and Applications

This paper discusses the mathematical theory of finite elements. Using the concepts of inner product spaces, the mathematics of finite element analysis is explained in the context of function spaces. The finite elements as well as the finite element space will be rigorously defined. Furthermore, examples from research in the field of engineering will be explained and viewed through a mathematical lens. This research paper seeks to firmly bridge the applications with mathematical content for the research scientist who generally focuses on the applications. The paper will begin with a review of some basic building blocks for the finite element space followed by validation of the process and construction of finite elements. The use of these elements will be compared. A trial will be done on the computer using a simple differential equation where the use of finite elements will be investigated for accuracy to validate the roof functions used in finite element analysis. Finally a short review of literature illustrating the technique will be presented

A stability version of H\"older's inequality

We present a stability version of H\"older's inequality, incorporating an extra term that measures the deviation from equality. Applications are given.Comment: Journal of Mathematical Analysis and Applications, Volume 343, Issue 2, Pages 842-852. This version differs from the published one in that it contains a new reference, and a trivial improvement of Corollary 3.2. fo