...distributivity.
The inner product is commonly written as the ``dot'' product: . We use the `dot'-notation exclusively for for inner products on vectors and (described below) use the `dot'-notation for the inner product on functions.
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...density
This relation between and is implicit in the variational method employed in [3].
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...zero
The integral over the boundary usually vanishes identically, either because admissible flows v vanish on (Dirichlet conditions), or because the function which is projected onto the boundary (which depends on derivatives of f with respect to its gradient and higher order-derivatives) in the boundary integral vanishes (Neumann conditions). If neither condition holds, then the boundary term must also be included in the variation.
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...equation
These equations, including the Allen-Cahn equation below, is sometimes written with -terms multiplying both the gradient term and the homogeneous part: . This form has some advantages for the investigation of asymptotic behavior of of small .
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```

W. Craig Carter
Tue Sep 30 16:07:27 EDT 1997