Is a curl-free vector field always a gradient? I tried to prove this problem using the Helmholtz decomposition theorem, but it seems the two are entirely contradictory--thus leaving me with empty hands. Does anyone know how to proceed?



Thanks

Moehringer
Read an answer here:      Helmholtz decomposition contradictions PDF http://analysis3.com/Helmholtz-decomposition-contradictions-pdf-e117376.html
Read an answer here:      Helmholtz decomposition contradictions PDF http://analysis3.com/Helmholtz-decomposition-contradictions-pdf-e117376.html