Abstract
Some results for the Hodge decomposition theorem in Euclidean three-space
Highlights
Let Ω be a bounded subset of three-space R3 and let V(x, y, z) be a vector field on Ω
In applications it is often useful to be able to determine whether V(x, y, z) is the gradient of a function, or the curl of another vector field, or perhaps a divergence-free field. The answer to such questions is based on an understanding of the relationship between vector calculus and the topology of their domains of definition [1]
The Hodge Decomposition theorem addresses these questions by studying the space of vector fields as a decomposition into five mutually orthogonal subspaces that are topologically and analytically significant
Summary
Follow this and additional works at: https://scholarworks.utrgv.edu/mss_fac Part of the Mathematics Commons. "Some Results for the Hodge Decomposition Theorem in Euclidean Three-Space." International Journal of Contemporary Mathematical Sciences 11.4 (2016): 155-164. International Journal of Contemporary Mathematical Sciences Vol 11, 2016, no. International Journal of Contemporary Mathematical Sciences Vol 11, 2016, no. 4, 155 - 164
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