On $L^{r}$ hypoellipticity of solutions with compact support of the Cauchy-Riemann equation
Langue
en
Article de revue
Ce document a été publié dans
Annali di Matematica Pura ed Applicata. 2014, vol. 193, n° 4, p. 999-1018
Springer Verlag
Résumé en anglais
In one complex variable, the existence of a compactly supported solution to the Cauchy-Riemann equation is related to the vanishing of certain integrals of the data; trying to generalize this approach, we find an explicit ...Lire la suite >
In one complex variable, the existence of a compactly supported solution to the Cauchy-Riemann equation is related to the vanishing of certain integrals of the data; trying to generalize this approach, we find an explicit construction, via convolution, for a compactly supported solution in TeX , which allows us to estimate the TeX norm of the solution. We also investigate the possible generalizations of this method to domains of the form TeX , where TeX is a polydisc and TeX is the zero locus of some holomorphic function.< Réduire
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