Let $\Omega\subset\mathbb{C}^n$ be a bounded domain with smooth boundary. We prove the existence of solutions for the equation $\partial \overline{\partial} u = f$ with trace $\gamma(u)$ on $b\Omega$ in the sense of distribution ([7]). Hence, given $g\in \mathcal{D}^\prime (b\Omega)$, we solve the Cauchy problem $\partial \overline{\partial} u = f , \gamma(u)=g$.
Un problema di Cauchy per l'operatore $\partial \overline{\partial}$
BARLETTA, Elisabetta
1986-01-01
Abstract
Let $\Omega\subset\mathbb{C}^n$ be a bounded domain with smooth boundary. We prove the existence of solutions for the equation $\partial \overline{\partial} u = f$ with trace $\gamma(u)$ on $b\Omega$ in the sense of distribution ([7]). Hence, given $g\in \mathcal{D}^\prime (b\Omega)$, we solve the Cauchy problem $\partial \overline{\partial} u = f , \gamma(u)=g$.File in questo prodotto:
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