摘要:

In this paper, we discuss some nonlinear Poincare boundary value problems for nonlinear uniformly elliptic equations of second order in a multiply connected domain by using the methods of complex functions. At first we propose some modified boundary value problems for nonlinear elliptic systems of first order and give a priori estimates of solutions for the modified problems. Afterwards applying the above results, the continuity method and Schauder fixed-point theorem, we prove that the above nonlinear Poincaré problems with some conditions has a solution.

ISSN:0278-1077    

DOI:10.1080/17476938508814105

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

摘要:

Special systems of PDE of the first order with constant coefficients take a simple form when written in the framework of the so-called biregular functions, which are defined in Euclidean space by means of generalized Cauchy Riemann operators.

ISSN:0278-1077    

DOI:10.1080/17476938508814106

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938508814107

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

摘要:

If Ω is a smoothly bounded pseudoconvex domain of finite type inand if Ω contains the origin, then the maximal ideal of functions inA(Ω) vanishing at the origin is generated by the coordinate functions.

ISSN:0278-1077    

DOI:10.1080/17476938508814108

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

摘要:

The univalent Bloch Constant is the smallest numberAsuch that there exists a function inSwhose image contains a disk of radiusAand no disk with larger radius. The best known upper bound for this number was 0.656468…. achieved by an example found by R. E. Goodman in 1945. An example is found giving a smaller upper bound, showing that Goodman's example is not extremal.

ISSN:0278-1077    

DOI:10.1080/17476938508814109

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

摘要:

It has been conjectured by Hummel, Scheinberg and Zalcman that iff(z) ≈a0+a1z+a2z2+ … is a nonvanishingHpfunction withthenfor alln⪖ 1 and 1 <p< ∞ where 1/p+ 1/q= 1. Using the Pontryagin Maximum Principle we solve a related extremal problem which proves the conjecture in the casen= 1 and in the case of arbitraryn⪖ 2 providedam= 0 for 1 ⩽m< (n1)/2.

ISSN:0278-1077    

DOI:10.1080/17476938508814110

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

摘要:

In this paper a class of complex measures is investigated and we prove a characterization theorem of this class via the Cauchy Transform.

ISSN:0278-1077    

DOI:10.1080/17476938508814111

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

摘要:

We prove that every value of anH1-function, taken at a point of the open unit disk, is equal to the average of the function on a boundary interval. It follows that the B.M.O. norm of any non-constant inner function is exactly equal to 1

ISSN:0278-1077    

DOI:10.1080/17476938508814112

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938508814113

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

摘要:

In this paper we define normal circular triangles and we show that Lehto's inner radius of univalence is 2k2for a normal circular triangle whose smallest interior angle iskπ. Using this result we show that the inner radius of univalence of a regularn-sided polygon is 2[(n-2)/n)2.

ISSN:0278-1077    

DOI:10.1080/17476938508814114

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor