A Kernel Approach to the Local Solvability of the Tangential Cauchy Riemann Equations

DOI10.2307/2000256zbMath0579.35062OpenAlexW4253711799MaRDI QIDQ3701862

Mei-Chi Shaw, Albert Boggess

Publication date: 1985

Full work available at URL: https://doi.org/10.2307/2000256

zbMATH Keywords

local solvabilitytangential Cauchy-Riemann equationsnonsolvabilityAndreotti-Hill's theoremexplicit integral kernel representations

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Holomorphic convexity (32E99) Envelopes of holomorphy (32D10) Geometric convexity in several complex variables (32F99) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Related Items

Kernels of Martinelli-Bochner type on hypersurfaces ⋮ Boundary Hölder and $L^p$ estimates for local solutions of the tangential Cauchy-Riemann equation ⋮ The range of the tangential Cauchy-Riemann operator over a small ball ⋮ Local existence theorems with estimates for \(\bar \partial_ b\) on weakly pseudo-convex CR manifolds ⋮ Fundamental solutions and optimal estimates for the tangential Cauchy-Riemann operator ⋮ \(L^ p\) estimates for local solutions of \({\bar \partial}_ b\) on strongly pseudo-convex CR-manifolds ⋮ Sobolev estimates for the local extension of ∂̄_{𝑏}-closed (0,1)-forms on real hypersurfaces in ℂⁿ with two positive eigenvalues ⋮ Unnamed Item ⋮ Optimal regularity for \(\overline\partial_b\) on CR manifolds

Cites Work

• Unnamed Item
• On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables
• On the local solvability and the local integrability of systems of vector fields
• Fundamental solutions in complex analysis. I. The Cauchy Riemann operator
• Kernels for the local solvability of the tangential Cauchy-Riemann equations
• A remark on the poincaré lenma in analytic complexes with nondegenerate levi form
• Kernels for the Tangential Cauchy-Riemann Equations
• The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)

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