How Are BV Functions Applied in Physics and Engineering?

[Hjensen]

I am reading about a branch of mathematics which does not allow separable spaces. The author of the text gives the space of functions of bounded variation as an example of a non-separable space, which is fine - except for the fact that he goes on to claim that "this space is relevant to both physicists and engineers" without giving any further elaboration.

So my question is this: Do any of you have a few examples of BV-functions being used in physics or engineering? I don't need a detailed explanation, I just need to convince myself that the argument given in my book is actually important.

 

[dlgoff]

The ability of BV functions to deal with discontinuities has made their use widespread in the applied sciences: solutions of problems in mechanics, physics, chemical kinetics are very often representable by functions of bounded variation. The book (Hudjaev & Vol'pert 1985) details a very ample set of mathematical physics applications of BV functions. Also there is some modern application which deserves a brief description.

http://en.wikipedia.org/wiki/Bounded_variation"

You might want to check out "Analysis in classes of discontinuous functions and equations of mathematical physics":
http://books.google.com/books?id=lA...tinuous+functions"&hl=en#v=onepage&q&f=false"

 

[Hjensen]

http://en.wikipedia.org/wiki/Bounded_variation"

You might want to check out "Analysis in classes of discontinuous functions and equations of mathematical physics":
http://books.google.com/books?id=lA...tinuous+functions"&hl=en#v=onepage&q&f=false"

I did have a look at Wikipedia before writing here. However, all it states is that BV functions have uses in mechanics, physics and chemical kinetics. I would have liked something a bit more specific. As for the book, it goes through the theory of BV - which I am already familiar with - but I can't find any physical applications of it. If you know a page number on which I could find this, I would appreciate it. Thanks for your time.

 

[dlgoff]

Page 326 talks about eigenvalues and eigenfunctions that are used in quantum physics.