IRIS Università degli Studi di Padovahttps://www.research.unipd.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Thu, 09 Apr 2020 08:54:06 GMT2020-04-09T08:54:06Z10841Subelliptic estimates and regularity of ∂¯ at the boundary of a Q-pseudoconvex domain of finite typehttp://hdl.handle.net/11577/2533368Titolo: Subelliptic estimates and regularity of ∂¯ at the boundary of a Q-pseudoconvex domain of finite type
Abstract: We prove subelliptic estimates in degree k ≥ q for the ¯∂-Neumann problem over a domain Ω ⊂⊂ Cn which is
weakly q-pseudoconvex and satisfies in addition a finite bracket type condition.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11577/25333682011-01-01T00:00:00ZThe Diederich–Fornaess index and the global regularity of the $$\bar{\partial }$$ ∂ ¯ -Neumann problemhttp://hdl.handle.net/11577/3156465Titolo: The Diederich–Fornaess index and the global regularity of the $$\bar{\partial }$$ ∂ ¯ -Neumann problem
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11577/31564652014-01-01T00:00:00ZAnalytic discs in pseudoconvex submanifolds of C^N of higher codimensionhttp://hdl.handle.net/11577/1428883Titolo: Analytic discs in pseudoconvex submanifolds of C^N of higher codimension
Abstract: We prove that a small analytic disc A “attached” to a pseudoconvex submanifold
M of CN and which shares a conormal with M at some boundary point, is in fact
contained in M. The proof uses an argument of “reduction to a hypersurface” by a symplectic
complex transformation. The result is classical in case codM = 1 (cf. e.g. [4]); it is
a consequence of Hopf’s Lemma applied to a plurisubharmonic defining function ofM as
in [5]. It was already generalized to the higher codimension in [8] but under the additional
assumption, in the present paper, that A has an analytic “lift” A
∗ in T
∗
X “attached” to
T
∗
MX (i.e. A has “defect” ≥ 1 in the terminology of [6], [7])
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11577/14288832005-01-01T00:00:00ZSubellipticity of the ∂¯-Neumann problem on a weakly q-pseudoconvex/concave domainhttp://hdl.handle.net/11577/2523787Titolo: Subellipticity of the ∂¯-Neumann problem on a weakly q-pseudoconvex/concave domain
Abstract: For a domain D of Cn which is weakly q-pseudoconvex or q-pseudoconcave, we give a sufficient condition for subelliptic estimates for the View the MathML source-Neumann problem. This extends to domains which are not necessarily pseudoconvex, the results and the techniques of Catlin (1987)
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11577/25237872011-01-01T00:00:00ZCompactness estimates for box-b on a CR manifoldhttp://hdl.handle.net/11577/2523794Titolo: Compactness estimates for box-b on a CR manifold
Abstract: This paper aims to state compactness estimates for the Kohn-Laplacian on an abstract CR manifold in full generality. The approach consists of a tangential basic estimate in the formulation given by the first author in his thesis, which refines former work by Nicoara. It has been proved by Raich that on a CR manifold of dimension $ 2n-1$ which is compact pseudoconvex of hypersurface type embedded in the complex Euclidean space and orientable, the property named ``$ (CR-P_q)$'' for $ 1\leq q\leq \frac {n-1}2$, a generalization of the one introduced by Catlin, implies compactness estimates for the Kohn-Laplacian $ \Box _b$ in any degree $ k$ satisfying $ q\leq k\leq n-1-q$. The same result is stated by Straube without the assumption of orientability. We regain these results by a simplified method and extend the conclusions to CR manifolds which are not necessarily embedded nor orientable. In this general setting, we also prove compactness estimates in degree $ k=0$ and $ k=n-1$ under the assumption of $ (CR-P_1)$ and, when $ n=2$, of closed range for $ {\bar \partial }_b$. For $ n\geq 3$, this refines former work by Raich and Straube and separately by Straube.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11577/25237942012-01-01T00:00:00ZAnalisi 2http://hdl.handle.net/11577/2482102Titolo: Analisi 2
Abstract: Libro di testo per corsi di Analisi Matematica 2
Sun, 01 Jan 1995 00:00:00 GMThttp://hdl.handle.net/11577/24821021995-01-01T00:00:00ZAnalytic discs under symplectic transformshttp://hdl.handle.net/11577/1566226Titolo: Analytic discs under symplectic transforms
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11577/15662262006-01-01T00:00:00ZComplex analysis and CR geometry.http://hdl.handle.net/11577/2429739Titolo: Complex analysis and CR geometry.
Abstract: ULECT: University Lecture Series
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11577/24297392008-01-01T00:00:00ZRays condition and extension of CR functions from manifolds of higher typehttp://hdl.handle.net/11577/2449935Titolo: Rays condition and extension of CR functions from manifolds of higher type
Abstract: We prove thatCRfunctions defined in awedge inside aCRmanifold
extend to be CR (or holomorphic) in the directions given by the higher order
generalization of the Levi form taken at complex tangent vectors satisfying the
so-called rays condition. This generalizes extension results by Boggess–Polking
[7], Baouendi–Treves [3], Fornaess–Rea [10] and the second and the third authors
[18] and puts them into a unified frame.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/11577/24499352007-01-01T00:00:00ZREGULARITY OF THE DI-BAR-NEUMANN PROBLEM AT A POINT OF INIFINITE TYPEhttp://hdl.handle.net/11577/2428680Titolo: REGULARITY OF THE DI-BAR-NEUMANN PROBLEM AT A POINT OF INIFINITE TYPE
Abstract: We introduce general estimates for “gain of regularity” of solutions of the ¯∂ -Neumann problem and relate
it to the existence of weights with large Levi form at the boundary. This enables us to discuss in a unified
framework the classical results on fractional ellipticity (= subellipticity), superlogarithmic ellipticity and
compactness. For each case, we exhibit a corresponding class of domains.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11577/24286802010-01-01T00:00:00Z