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$C^{k}$ -estimates for the $\bar{\partial}$ -equation on concave domains of finite type

William Alexandre (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

$C^{k}$ estimates for convex domains of finite type in $ℂ^{n}$ are known from [7] for $k = 0$ and from [2] for $k > 0$ . We want to show the same result for concave domains of finite type. As in the case of strictly pseudoconvex domain, we fit the method used in the convex case to the concave one by switching $z$ and $ζ$ in the integral kernel of the operator used in the convex case. However the kernel will not have the same behavior on the boundary as in the Diederich-Fischer-Fornæss-Alexandre work. To overcome this problem...

$C^{k}$ -regularity for the $\bar{\partial}$ -equation on a piecewise smooth union of strictly pseudoconvex domains in $ℂ^{n}$

Joachim Michel, Alessandro Perotti (1994)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Canonical homotopy operators for the $\bar{\partial}$ complex in strictly pseudoconvex domains

Mats Andersson, Jörgen Boo, Joaquim Ortega-Cerdà (1998)

Bulletin de la Société Mathématique de France

Ck-Regularity for the ?-equation on Strictly Pseudoconvex Domains with Piecewise Smooth Boundaries.

Joachim Michel, Alessandro Perotti (1990)

Mathematische Zeitschrift

Cohomologie de dolbeault le long des feuilles de certains feuilletages complexes

Aziz El Kacimi Alaoui, Jihène Slimène (2010)

Annales de l’institut Fourier

La cohomologie de Dolbeault feuilletée mesure l’obstruction à résoudre le problème de Cauchy-Riemann le long des feuilles d’un feuilletage complexe. En utilisant des méthodes de cohomologie des groupes, nous calculons cette cohomologie pour deux classes de feuilletages : i) le feuilletage complexe affine de Reeb de dimension (complexe) 2 sur la variété de Hopf de dimension 5 ; ii) les feuilletages complexes sur le tore hyperbolique (fibration en tores de dimension n au-dessus d’un cercle et de monodromie...

Cohomology with $L^{p}$ -bounds on polycylinders.

Darko, P.W., Lutterodt, C.H. (1995)

International Journal of Mathematics and Mathematical Sciences

Convexité et equations de Cauchy-Riemann avec estimations Lp.

Corinne Jouenne (2000)

Publicacions Matemàtiques

We obtain a solution of the equation ∂u = f as an integral supported only on the bounded convex domain D of Cn, without finite type assumption.

Correction to my Paper "Intrinsic Lipschitz Classes on Manifolds with Applications to Complex Function Theory and Estimates for the ... and ... Equations". (Correction)

Steven G. Krantz (1979)

Manuscripta mathematica

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