Mathematics, 06.04.2021 04:30 anele22

Suppose U1 and U2 are two open sets in R^n with U1âˆ©U2 non-empty and path connected. Suppose there exists an f1 : U1 â†’ R and f2 : U2 â†’ R, both twice continuously differentiable such that d f1 = d f2 on U1 âˆ© U2. Then there exists a twice differentiable function F : U1 âˆªU2 â†’ R such that dF = d f1 on U1 and dF = d f2 on U2

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Suppose U1 and U2 are two open sets in R^n with U1âˆ©U2 non-empty and path connected. Suppose there...