Extended shockwave decomposability related to boundaries of holomorphic 1-chains within $\mathbb{CP}^2$
Ronald Walker
32C3035Q5335N10boundaries of holomorphic chainsBurgers equationsums of shockwavesoverdetermined systems
We consider the notion of meromorphic Whitney multifunction solutions to $ff_{\xi} = f_{\eta}$, which yields an enhanced version of the Dolbeault Henkin characterization of boundaries ofholomorphic 1-chains within $\mathbb{C}\mathbb{P}^2$. By analyzing the equations describing meromorphic Whitney multifunction solutions to $ff_{\xi} = f_{\eta}$ and by creating some generalizationsof certain linear dependence results, we show that a function $G$ may be decomposed into a sum of such solutions, modulo $\xi$-affine functions and with a selected bound on the degree of such sum, if and only if $G_{\xi\xi}$ satisfies a finite set of explicitly constructible partial differential equations.
Indiana University Mathematics Journal
2008
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10.1512/iumj.2008.57.3221
10.1512/iumj.2008.57.3221
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Indiana Univ. Math. J. 57 (2008) 1133 - 1172
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