Résolution du pour les courants prolongeables définis dans un anneau
Résolution du pour les formes différentielles ayant une valeur au bord au sens des courants dans un domaine strictement pseudoconvexe
On résout le pour les formes admettant une valeur au bord au sens des courants sur un domaine strictement pseudoconvexe de .
Résolution locale du ... avec régularité Gevrey au bord d'un domaine r-convexe.
Semi-global solutions of ∂b with Lp (1 ≤ p ≤ ∞) bounds on strongly pseudoconvex real hypersurfaces in Cn (n ≥ 3).
Let M be an open subset of a compact strongly pseudoconvex hypersurface {ρ = 0} defined by M = D × Cn-m ∩ {ρ = 0}, where 1 ≤ m ≤ n-2, D = {σ(z1, ..., zm) < 0} ⊂ Cm is strongly pseudoconvex in Cm. For ∂b closed (0, q) forms f on M, we prove the semi-global existence theorem for ∂b if 1 ≤ q ≤ n-m-2, or if q = n - m - 1 and f satisfies an additional “moment condition”. Most importantly, the solution operator satisfies Lp estimates for 1 ≤ p ≤ ∞ with p = 1 and ∞ included.
Seperable maximal pluriharmonic functions in two complex variables.
Sharp Hölder Estimates for ... on Ellipsoides.
Singularity and regularity -- local and global.
Sobolev cohomology for locally polycylindrical domains.
Sobolev Estimates for the Lewy Operator on Weakly Pseudo-Convex Boundaries.
Sobolev estimates for the ?-Neumann operator on domains in Cn admitting a defining function that is plurisubharmonic on the boundary.
Sobolev space estimates for solutions of the equation on polycylinders.
Solution of the ?-Equation with Uniform Estimates on Strictly q-Convex Domains with Non-Smooth Boundary.
Solution operators for the ...-equation on non-transversal intersections.
Solutions de l’équation et zéros de la classe de Nevanlinna dans certains domaines faiblement pseudo-convexes
Il est montré que la condition de Blaschke est nécessaire et suffisante pour qu’un sous-ensemble analytique du domaine soit l’ensemble des zéros d’une fonction de la classe de Nevanlinna.
Solutions to -equations on strongly pseudo-convex domains with -estimates.
Some applications of a new integral formula for
Let M be a smooth q-concave CR submanifold of codimension k in . We solve locally the -equation on M for (0,r)-forms, 0 ≤ r ≤ q-1 or n-k-q+1 ≤ r ≤ n-k, with sharp interior estimates in Hölder spaces. We prove the optimal regularity of the -operator on (0,q)-forms in the same spaces. We also obtain estimates at top degree. We get a jump theorem for (0,r)-forms (r ≤ q-2 or r ≥ n-k-q+1) which are CR on a smooth hypersurface of M. We prove some generalizations of the Hartogs-Bochner-Henkin extension...
Some applications of the trace condition for pluriharmonic functions in Cn.
In this paper we investigate some applications of the trace condition for pluriharmonic functions on a smooth, bounded domain in Cn. This condition, related to the normal component on ∂D of the ∂-operator, permits us to study the Neumann problem for pluriharmonic functions and the ∂-problem for (0,1)-forms on D with solutions having assigned real part on the boundary.
Some characterizations of the class and applications
We give some characterizations of the class and use them to establish a lower estimate for the log canonical threshold of plurisubharmonic functions in this class.
Some open problems in higher dimensional complex analysis and complex dynamics.
We present a collection of problems in complex analysis and complex dynamics in several variables.
Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator
We find a bounded solution of the non-homogeneous Monge-Ampère equation under very weak assumptions on its right hand side.