On $L^{r}$ hypoellipticity of solutions with compact support of the Cauchy-Riemann equation

Eric Amar (1) , Samuel Mongodi (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Scuola Superiore di Pisa

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.

Domaines: Variables complexes [math.CV]

Eric Amar, Samuel Mongodi. On $L^{r}$ hypoellipticity of solutions with compact support of the Cauchy-Riemann equation. Annali di Matematica Pura ed Applicata, 2014, 193 (4), pp.999-1018. ⟨10.1007/s10231-012-0312-8⟩. ⟨hal-01022852⟩