Some natural applications include:

The parts of specifications given directly in terms of numerical inequalities

Heavy numerical processing with lots of conditional logic: tax forms, payroll processing, financial calculations, most things you do with a spreadsheet.

Numerical inputs and heavy input validation and categorization, even if the subsequent processing isn't intensively numerical.

Don't restrict your notion and application of domain testing to software.

Bug assumptions:

Domain specification bugs: Ambiguous domains - the specification of the input space is incomplete; contradictory domains - domains overlap, especially at boundaries with closure to both sides; over specified domains - too many inequalities conspire to define a domain out of existence; degenerate domains where not intended.

Domain boundary bugs: These bugs include, in a typical order of likelihood and importance: wrong closure, shift, tilt, missing boundary, extra boundary

Domain processing bugs: Here domains appear to be correctly specified but the processing function is wrong for the domain. Wrong function chosen is likelier than an error in the implementation of the function.

Domain vertex bugs: These are expressed only at the vertex points of specified domains, especially if there's a lot of ad-hoc logic.

Limitations and Caveats:

Loops: It's assumed that there are no loops in the domain selection processing. Loops within the domain processing are okay as long as you can guarantee that once in a given domain, the processing will never cause the program to leave that domain.

Coincidental correctness: a problem for all test techniques. The likeliest situation is coincidental correctness with respect to input domains. That is, because of coincidental correctness, bad inputs are rejected for the wrong reasons.

Blindness limits and epsilon: Domain testing is blind to errors of less than your chosen epsilon. You may not be able to pick a single value for all your testing. Your processing might push the limits of small numbers in your system and an appropriate epsilon can cause underflow.

Difficulty with OFF point selection for closed domains: For domains that have boundaries with input rejection domains, the OFF point may tell you nothing because the input validation occurs before domain selection.