The∂b-Neumann problem on noncharacteristic domains
نویسندگان
چکیده
منابع مشابه
∂̄b-NEUMANN PROBLEM ON NONCHARACTERISTIC DOMAINS
We study the ∂̄b-Neumann problem for domains Ω contained in a strictly pseudoconvex manifold M2n+1 whose boundaries are noncharacteristic and have defining functions depending solely on the real and imaginary parts of a single CR function w. When the Kohn Laplacian is a priori known to have closed range in L2, we prove sharp regularity and estimates for solutions. We establish a condition on the...
متن کاملThe Neumann Problem on Lipschitz Domains
Au — 0 in D; u = ƒ on bD9 where ƒ and its gradient on 3D belong to L(do). For C domains, these estimates were obtained by A. P. Calderón et al. [1]. For dimension 2, see (d) below. In [4] and [5] we found an elementary integral formula (7) and used it to prove a theorem of Dahlberg (Theorem 1) on Lipschitz domains. Unknown to us, this formula had already been discovered long ago by Payne and We...
متن کاملGlobal C∞ Irregularity of the ∂̄–neumann Problem for Worm Domains
where ρ is a defining function for Ω, = ∂̄∂̄∗ + ∂̄∗∂̄, u, f are (0, 1) forms, and denotes the interior product of forms. Under the stated hypotheses on Ω, this problem is uniquely solvable for every f ∈ L(Ω). The Neumann operator N , mapping f to the solution u, is continuous on L(Ω). The Bergman projection B is the orthogonal projection of L(Ω) onto the closed subspace of L holomorphic functions o...
متن کاملOn Neumann Eigenfunctions in Lip Domains
A planar set D will be called a lip domain if it is Lipschitz, open, bounded, connected, and given by (1) D = {(x1, x2) : f1(x1) < x2 < f2(x1)}, where f1, f2 are Lipschitz functions with constant 1. The assumption that D is a Lipschitz domain puts an extra constraint on the functions fk; we discuss this issue in greater detail later in this section. Let μ2 denote the second eigenvalue for the L...
متن کاملA Remark on Irregularity of the ∂-neumann Problem on Non-smooth Domains
It is an observation due to J.J. Kohn that for a smooth bounded pseudoconvex domain Ω in C there exists s > 0 such that the ∂-Neumann operator on Ω maps W s (0,1)(Ω) (the space of (0, 1)-forms with coefficient functions in L -Sobolev space of order s) into itself continuously. We show that this conclusion does not hold without the smoothness assumption by constructing a bounded pseudoconvex dom...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2009
ISSN: 0030-8730
DOI: 10.2140/pjm.2009.242.71