The Martin compactification of a plane domain

Third order initial boundary value problem is studied in a bounded plane domain σ with C4 smooth boundary ∂σ. The existence and uniqueness of the solution is proved using Galerkin approximations and a priory estimates. The problem under consideration appear as an auxiliary problem by studying a second grade fluid motion in an infinite three-dimensional pipe with noncircular cross-section.

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Water adsorption induced in-plane domain switching on BaTiO3 surface

Journal of Applied Physics ◽

10.1063/1.4930035 ◽

2015 ◽

Vol 118 (9) ◽

pp. 094104 ◽

Cited By ~ 5

Author(s):

X. Li ◽

Y. Bai ◽

B. C. Wang ◽

Y. J. Su

Keyword(s):

Water Adsorption ◽

Domain Switching ◽

Plane Domain

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Microscopic Liquid Crystal Theory of Nematic Reentrance, Smectic C Ordering, and In-Plane Domain Formation

NATO ASI Series - Phase Transitions in Liquid Crystals ◽

10.1007/978-1-4684-9151-7_7 ◽

1992 ◽

pp. 109-124 ◽

Cited By ~ 1

Author(s):

R. R. Netz ◽

A. N. Berker

Keyword(s):

Liquid Crystal ◽

Plane Domain ◽

Domain Formation ◽

Smectic C

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Projections on Bergman Spaces Over Plane Domains

Canadian Journal of Mathematics ◽

10.4153/cjm-1979-105-6 ◽

1979 ◽

Vol 31 (6) ◽

pp. 1269-1280 ◽

Cited By ~ 1

Author(s):

Jacob Burbea

Keyword(s):

Bergman Kernel ◽

Bergman Spaces ◽

Holomorphic Functions ◽

Plane Domain ◽

Bergman Projection ◽

Lebesgue Spaces ◽

Lebesque Measure ◽

Image Position

Let D be a bounded plane domain and let Lp(D) stand for the usual Lebesgue spaces of functions with domain D, relative to the area Lebesque measure dσ(z) = dxdy. The class of all holomorphic functions in D will be denoted by H(D) and we write Bp(D) = Lp(D) ∩ H(D). Bp(D) is called the Bergman p-space and its norm is given byLet be the Bergman kernel of D and consider the Bergman projection(1.1)It is well known that P is not bounded on Lp(D), p = 1, ∞, and moreover, it can be shown that there are no bounded projections of L∞(Δ) onto B∞(Δ).

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