Search Results - \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs

SOBOLEV ESTIMATES OF SOLUTIONS OF THE $\bar{\partial}$-NEUMANN PROBLEM ON PARAMETERS: Sobolev estimates of solutions of the \(\overline\partial\)-Neumann problem on parameters.

Authors: Sanghyun Cho

Source: International Journal of Mathematics. 13:1027-1042

Subject Terms: \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Cauchy-Riemann equations. Sobolev spaces, 01 natural sciences

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Access URL: http://www.worldscientific.com/doi/abs/10.1142/S0129167X02001587

Estimates on the heat kernel of the Pauli Hamiltonian and its application to problems on hypoellipticity of the $\overline{\partial _b}$ -Laplacian: Estimates on the heat kernel of the Pauli Hamiltonian and its application to problems on hypoellipticity of the \(\overline\partial_b\)-Laplacian.

Authors: Naomasa Ueki

Source: Mathematische Zeitschrift. 239:69-97

Subject Terms: \(\overline\partial_b\) and \(\overline\partial_b\)-Neumann operators, heat kernel, 0103 physical sciences, hypoellipticity, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, Heat kernels in several complex variables, \(\overline \partial_b\)-Laplacian, 01 natural sciences, Pauli Hamiltomian

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Access URL: https://zbmath.org/1716689
https://doi.org/10.1007/s002090100283
https://link.springer.com/content/pdf/10.1007/s002090100283.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=2806628
https://link.springer.com/article/10.1007/s002090100283

Plurisubharmonic functions and subellipticity of the $\bar\partial$-Neumann problem on non-smooth domains: Plurisubharmonic functions and subellipticity of the \(\bar\partial\)-Neumann problem on non-smooth domains

Authors: Emil J. Straube

Source: Mathematical Research Letters. 4:459-467

Subject Terms: reglarity, \(\overline \partial\)-Neumann problem, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Plurisubharmonic functions and generalizations, approximation, 01 natural sciences, subelliptic estimate, finite type

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Access URL: http://www.intlpress.com/site/pub/files/_fulltext/journals/mrl/1997/0004/0004/MRL-1997-0004-0004-a002.pdf
https://zbmath.org/1082973
https://doi.org/10.4310/mrl.1997.v4.n4.a2
http://www.intlpress.com/site/pub/pages/journals/items/mrl/content/vols/0004/0004/a002/
https://ui.adsabs.harvard.edu/abs/1996math.....12205S/abstract
https://www.intlpress.com/site/pub/files/_fulltext/journals/mrl/1997/0004/0004/MRL-1997-0004-0004-a002.pdf

The $\overline {\partial }$ problem on domains with piecewise smooth boundaries with applications: The \(\overline\partial\) problem on domains with piecewise smooth boundaries with applications

Authors: Mei-Chi Shaw Joachim Michel

Source: Transactions of the American Mathematical Society. 351:4365-4380

Subject Terms: \(q\)-convexity, \(q\)-concavity, tangential Cauchy-Riemann equations, Nonlinear first-order PDEs, Overdetermined systems of PDEs with constant coefficients, Overdetermined systems of PDEs with variable coefficients, Cauchy-Riemann equations, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, 01 natural sciences

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Access URL: https://www.ams.org/tran/1999-351-11/S0002-9947-99-02519-2/S0002-9947-99-02519-2.pdf
https://zbmath.org/1329214
https://doi.org/10.1090/s0002-9947-99-02519-2
https://dialnet.unirioja.es/servlet/articulo?codigo=477219
https://www.ams.org/journals/tran/1999-351-11/S0002-9947-99-02519-2/home.html
https://www.ams.org/tran/1999-351-11/S0002-9947-99-02519-2/S0002-9947-99-02519-2.pdf

The union problem on complex manifolds

Authors: Patrick W. Darko

Source: International Journal of Mathematics and Mathematical Sciences, Vol 30, Iss 10, Pp 621-625 (2002)

Subject Terms: \(L^2\)-estimates, Analytic sheaves and cohomology groups, QA1-939, Stein spaces, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, 01 natural sciences, Mathematics, union of Stein open sets

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Access URL: http://downloads.hindawi.com/journals/ijmms/2002/324610.pdf
https://zbmath.org/1779145
https://doi.org/10.1155/s0161171202007603
https://doaj.org/article/c43386c924f44fa3a5110ea65bb9933b
https://downloads.hindawi.com/journals/ijmms/2002/324610.pdf
https://www.emis.de/journals/HOA/IJMMS/Volume30_10/625.pdf
http://downloads.hindawi.com/journals/ijmms/2002/324610.pdf
https://www.hindawi.com/journals/ijmms/2002/324610/

The $\overline\partial$-Neumann problem in the Sobolev topology: The \(\overline\partial\)-Neumann problem in the Sobolev topology

Authors: FONTANA, LUIGI Krantz, SG Peloso, MM

Subject Terms: Hypoelliptic equations, boundary value problem, Neumann problem, Pseudoconvex domains, Other notions of convexity in relation to several complex variables, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, modified \(\overline\partial\)-Neumann problem

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Access URL: https://zbmath.org/1366161
https://hdl.handle.net/10281/17818

Good Stein neighborhood bases and regularity of the $\overline\partial$-Neumann problem: Good Stein neighborhood bases and regularity of the \(\overline{\partial}\)-Neumann problem

Authors: Straube, Emil J.

Source: Illinois J. Math. 45, no. 3 (2001), 865-871

Subject Terms: 32W05, Stein neighborhood, 35N15, 32T99, Pseudoconvex domains, \(\bar\partial\)-Neumann problem, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Sobolev space, 01 natural sciences

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Access URL: https://zbmath.org/1699485
https://projecteuclid.org/download/pdf_1/euclid.ijm/1258138156
https://projecteuclid.org/journals/illinois-journal-of-mathematics/volume-45/issue-3/Good-Stein-neighborhood-bases-and-regularity-of-the-overlinepartial-Neumann/10.1215/ijm/1258138156.full
http://projecteuclid.org/euclid.ijm/1258138156

Global regularity of the $$\bar \partial $$ -Neumann problem on circular domains: Global regularity of the \(\overline{\partial}\)-Neumann problem on circular domains

Authors: So-Chin Chen

Source: Mathematische Annalen. 285:1-12

Subject Terms: Reinhardt pseudoconvex domain, Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube), 0103 physical sciences, Pseudoconvex domains, global regularity of the \(\overline{\partial }\)-Neumann problem, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, pseudoconvex circular domain, 01 natural sciences

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Access URL: https://zbmath.org/4081958
https://doi.org/10.1007/bf01442668
https://eudml.org/doc/164581
https://link.springer.com/article/10.1007%2FBF01442668

hodge theory in the sobolev topology for the de rham complex on a smoothly bounded domain in euclidean space: Hodge theory in the Sobolev topology for the de Rham complex on a smoothly bounded domain in Euclidean space

Authors: FONTANA, LUIGI Krantz, SG Marco, M.

Source: Electronic Research Announcements of The American Mathematical Society. 1(3):103-107

Subject Terms: Boundary value problems for PDEs with pseudodifferential operators, a priori estimate in the Sobolev-topology, de Rham complex, Boundary value problems for second-order elliptic equations, Differential complexes, Hodge theory in global analysis, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, subelliptic estimate

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Access URL: https://www.ams.org/journals/era/1995-01-03/S1079-6762-95-03002-2/home.html
https://boa.unimib.it/handle/10281/17815?mode=full.2
https://www.ams.org/era/1995-01-03/S1079-6762-95-03002-2/S1079-6762-95-03002-2.pdf
https://hdl.handle.net/10281/17815

SOLUTIONS TO ${\bar\partial}$-EQUATION ON STRONGLY q-CONVEX DOMAINS WITH Lp-ESTIMATES: Solutions to \(\overline\partial\)-equation on strongly \(q\)-convex domains with \(L^p\)-estimates

Authors: Osama Abdelkader Shaban Khidr

Source: International Journal of Geometric Methods in Modern Physics. :739-749

Subject Terms: \(\bar\partial\)-equation, \(q\)-convex, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, A priori estimates in context of PDEs, 01 natural sciences

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Access URL: https://www.worldscientific.com/doi/abs/10.1142/S0219887804000368
http://ui.adsabs.harvard.edu/abs/2004IJGMM..01..739A/abstract

Partial regularity for homogeneous complex Monge–Ampere equations: Partial regularity for homogeneous complex Monge-Ampère equations

Authors: Gang Tian Xiuxiong Chen

Source: Comptes Rendus. Mathématique. 340:337-340

Subject Terms: Complex Monge-Ampère operators, almost smooth solution, partial regularity, Monge-Ampère equation, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, 01 natural sciences

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Access URL: https://www.sciencedirect.com/science/article/pii/S1631073X04005771

Green's Formulas in Complex Analysis: Green's formulas in complex analysis

Authors: Nikolai N. Tarkhanov Alexander Shlapunov

Source: Journal of Mathematical Sciences. 120:1868-1900

Subject Terms: Cauchy problem, Dolbeault complex, CR structures, CR operators, and generalizations, Green's formulas, Differential complexes, Fredholm problem, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.), 01 natural sciences

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Access URL: https://zbmath.org/2170263
https://doi.org/10.1023/b:joth.0000020708.24761.bb
https://link.springer.com/article/10.1023/B:JOTH.0000020708.24761.bb

The explicit solutions of $$C_{p,q}^{k + \alpha } $$ -form for the $$\bar \partial $$ -equations on pseudoconvex open sets: The explicit solutions of \(C_{p,q}^{k+\alpha}\)-form for the \(\overline{\partial}\)-equations on pseudoconvex open sets

Authors: Zhongtai Ma

Source: Acta Mathematicae Applicatae Sinica. 13:130-135

Subject Terms: Levi form, Cauchy-Riemann equations, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, pseudoconvex domains, 01 natural sciences, \(\overline\partial\) problem

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Access URL: https://link.springer.com/article/10.1007/BF02015134

Some aspects of Property for: Some aspects of Property \((P_q)\) for \(q>1\)

Authors: Yue Zhang

Source: Mathematische Nachrichten. 290:1119-1134

Subject Terms: fine topology, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, 16. Peace & justice, pseudoconvex domains, 01 natural sciences, \(\bar \partial\)-Neumann operator

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Access URL: https://rss.onlinelibrary.wiley.com/doi/am-pdf/10.1002/mana.201400402
https://zbmath.org/6737318
https://doi.org/10.1002/mana.201400402
https://ideas.repec.org/a/bla/mathna/v290y2017i7p1119-1134.html

On Iterations of the Green Integrals and their Applications to Elliptic Differential Complexes: On iterations of the Green integrals and their applications to elliptic differential complexes

Authors: Mauro Nacinovich Alexandre Shlapunov

Source: Mathematische Nachrichten. 180:243-284

Subject Terms: Poincaré's lemma, Overdetermined systems of PDEs with variable coefficients, first Sobolev cohomology group, Systems of elliptic equations, boundary value problems, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, elliptic differential complexes, 0101 mathematics, 01 natural sciences

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Access URL: http://onlinelibrary.wiley.com/doi/10.1002/mana.3211800111/abstract
https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fmana.3211800111

The Dolbeault complex in infinite dimensions I: The Dolbeault complex in infinite dimensions. I

Authors: László Lempert

Source: Journal of the American Mathematical Society. 11:485-520

Subject Terms: Mathematics - Complex Variables, Applications of analytic spaces to physics and other areas of science, Cauchy-Riemann equations, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, Infinite-dimensional holomorphy, 01 natural sciences, Functional Analysis (math.FA), Mathematics - Functional Analysis, Banach spaces, 32F15, 46G20, \(\overline{\partial}\) equation, Dolbeault cohomology, FOS: Mathematics, Complex Variables (math.CV), 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators

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Access URL: https://www.ams.org/jams/1998-11-03/S0894-0347-98-00266-5/S0894-0347-98-00266-5.pdf
https://www.ams.org/jams/1999-12-03/S0894-0347-99-00296-9/S0894-0347-99-00296-9.pdf
http://arxiv.org/abs/math/9803117
https://zbmath.org/1165759
https://doi.org/10.1090/s0894-0347-98-00266-5
https://arxiv.org/pdf/math/9803117
https://dialnet.unirioja.es/servlet/articulo?codigo=459756
https://www.ams.org/jams/1998-11-03/S0894-0347-98-00266-5/S0894-0347-98-00266-5.pdf
https://www.jstor.org/stable/pdfplus/2646159.pdf
https://www.arxiv-vanity.com/papers/math/9803117/
https://www.ams.org/journals/jams/1998-11-03/S0894-0347-98-00266-5/

The Green Function of Model Step Two Hypoelliptic Operators and the Analysis of Certain Tangential Cauchy Riemann Complexes: The Green function of model step two hypoelliptic operators and the analysis of certain tangential Cauchy Riemann complexes

Authors: Richard Beals Bernard Gaveau Peter Greiner

Source: Advances in Mathematics. 121:288-345

Subject Terms: Mathematics(all), Analysis on other specific Lie groups, Lie algebra, Numerical computation of solutions to systems of equations, hypoelliptic operators, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, Heisenberg group, 01 natural sciences, Dynamical systems with hyperbolic behavior, heat kernel, Pseudodifferential operators and other generalizations of partial differential operators, nilpotent Lie group, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators

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Access URL: https://zbmath.org/934301
https://doi.org/10.1006/aima.1996.0054
https://core.ac.uk/display/82171879
https://www.sciencedirect.com/science/article/pii/S0001870896900547
http://www.sciencedirect.com/science/article/pii/S0001870896900547

Homotopy formulas for $\bar\partial_b$ in $CR$ manifolds with mixed Levi signatures: Homotopy formulas for \(\overline{\partial}_ b\) in \(CR\) manifolds with mixed Levi signatures

Authors: Mei-Chi Shaw

Source: Mathematische Zeitschrift. 224:113-135

Subject Terms: integral kernels, local solution, Integral representations, canonical kernels (Szegő, Bergman, etc.), Cauchy-Riemann equations, CR manifolds, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, homotopy formulas, 01 natural sciences

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Access URL: https://zbmath.org/1028144
https://doi.org/10.1007/pl00004285
https://link.springer.com/article/10.1007%2FPL00004285

A division problem for $$\bar \partial _b - CLOSED$$ forms: A division problem for \(\bar \partial_ b\)-closed forms

Authors: Mats Andersson

Source: Journal d'Analyse Mathématique. 68:39-58

Subject Terms: division problem, Corona problem, Boundary behavior of holomorphic functions of several complex variables, \(\overline\partial_ b\)-closed forms, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/927194
https://doi.org/10.1007/bf02790203
https://link.springer.com/article/10.1007%2FBF02790203

Regular functions of several quaternionic variables and the Cauchy-Fueter complex

Authors: W. W. Adams C. A. Berenstein P. Loustaunau et al.

Source: Journal of Geometric Analysis. 9:1-15

Subject Terms: new duality theorems, 0103 physical sciences, Differential complexes, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, Hartogs theorem, 01 natural sciences, Generalized function theory, matrix techniques

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Access URL: https://zbmath.org/1542090
https://doi.org/10.1007/bf02923085
https://link.springer.com/article/10.1007/BF02923085
https://link.springer.com/content/pdf/10.1007/BF02923085.pdf