A Remark on Tonelli’s Calculus of Variations

A remark on the H∞-calculus

If A,B are sectorial operators on a Hilbert space with the same domain and range, and if �Ax� ≈ �Bx� and �A−1x� ≈ �B−1x�, then it is a result of Auscher, McIntosh and Nahmod that if A has an H ∞−calculus then so does B. On an arbitrary Banach space this is true with the additional hypothesis on B that it is almost R-sectorial as was shown by the author, Kunstmann and Weis in a recent preprint. ...

Forsyth on Calculus of Variations

It is therefore wholly to its credit tha t Bell's book is so largely abstract . In this way he has secured the utmost generality and hence insured permanency to his work. There is also the following important immediate gain. After constructing abstract theories for various classes of problems, he was in a position to decide if those theories are distinct or are (abstractly) identical. In the la...

An analytic study on the Euler-Lagrange equation arising in calculus of variations

The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...

Tonelli on Calculus of Variations 3 8 1 Tonelli on Calculus of Variations

denoising medical images using calculus of variations

we propose a method for medical image denoising using calculus of variations and local variance estimation by shaped windows. this method reduces any additive noise and preserves small patterns and edges of images. a pyramid structure-texture decomposition of images is used to separate noise and texture components based on local variance measures. the experimental results show that the proposed...