Partial differential equations in several complex variables

By So-chin Chen, Mei-Chi Shaw. 2001

542 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9ab4340a721990cded86607f1cea37036abdb198

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Projections in several complex variables (2008, methodology): “General references for this section are the books by Hörmander [15], Folland-Kohn [9] and Chen-Shaw [3].”
Estimates for the -Neumann problem and nonexistence of C2 Levi-flat hypersurfaces in (2004, methodology): “Theorem 3.1.14 in Folland-Kohn [FK] or Theorem 4.4.3 in [ CS ])”
Compactness of the solution operator to ∂¯ in weighted L2-spaces☆ (2007, unknown): “If v is a closed (0, q + 1)-form, then ∂∗Nq+1v provides the canonical solution to ∂u = v, which is orthogonal to the kernel of ∂ and so has minimal norm (see for instance [7]).”
Sharp constants for Moser‐Trudinger inequalities on spheres in complex space ℂn (2004, background): “Motivated by [17], the prominent role of the Heisenberg group H and the sphere in C in CR geometry, and the intimate relationship between them (see expositions for such a relationship in [16, 37]), in this paper we investigate the sharp Moser-Trudinger and Moser-Onofri inequalities on the sphere in ”
A sufficient condition for global regularity of the ∂¯-Neumann operator (2008, background): “functions and/or vector fields that commute approximately with ∂ due to Boas and the author [4, 6].”
Embeddability for Three-Dimensional Cauchy-Riemann Manifolds and CR Yamabe Invariants (2010, methodology): “Thus by using the construction of Boutet de Monvel in [4] or the exposition of Chen and Shaw in [7], we can embed for " > 0 small enough the CR structures via a map ‰t into the same C , that is, ‰t W .”
Global regularity for ∂¯b on weakly pseudoconvex CR manifolds☆ (2006, result): “1 of [3]) that closeness of range in H of ̄ ∗ b,t is equivalent to the following estimate for s 1 〈| s−1 t |〉t Ct 〈| s−1ut |〉t .”
Analysis of the Kohn Laplacian on quadratic CR manifolds (2003, methodology): “We refer the reader to the monographs [B], [ChSh] and to [AK] for accounts on these matters.”
Analysis and Geometry on Worm Domains (2007, background): “K−1(ζ, ω) = (|ζ1||ω1|) −1 · ( |ω1|β |ζ1|β + O(|ω1| β/|ζ1| νβ ) ) · (ζ2ω̄2) −1 , with ν > νβ , as |ζ1| − |ω1| → 0 , The proof of these two assertions can be found in [Ba3] (or see [CheS]).”