Analytic continuation and boundary continuity of functions of several complex variables

1981 ◽  
Vol 89 (1-2) ◽  
pp. 63-74 ◽  
Author(s):  
Edgar Lee Stout
Keyword(s):  
Analytic Continuation ◽  
Extension Property ◽  
Local Version ◽  
Boundary Values ◽  
One Dimensional ◽  
Several Variables ◽  
Bounded Holomorphic Function ◽  
The One ◽  
Bounded Holomorphic ◽  
Hartogs Theorem

SynopsisThis note treats some questions about analytic continuation in several variables. The first theorem in effect determines the envelops of holomorphy of certain domains in ℂn. The second main result is a continuity theorem: If a bounded holomorphic function f on a convex domain ∆ in ℂn has boundary values that are continuous on the complement (in b∆) of a set of the form int∏ (b∆∩∏) where ∏ is a real hyperplane in ℂn that misses ∆, then f is continuous on . In addition, we obtain what may be regarded as a local version of the theorem in our earlier paper concerning the one-dimensional extension property. Our methods depend on Hartogs' theorem (n ≧ 3) and directly on the BochnerMartinelli formula (n = 2).

scholarly journals Uniqueness and stability of solutions for a type of parabolic boundary value problem

1989 ◽  
Vol 12 (4) ◽  
pp. 735-739
Author(s):  
Enrique A. Gonzalez-Velasco
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Nonnegative Solution ◽  
Boundary Value ◽  
Stability Of Solutions ◽  
General Boundary Conditions ◽  
Boundary Values ◽  
Parabolic Boundary ◽  
One Dimensional ◽  
The One

We consider a boundary value problem consisting of the one-dimensional parabolic equationgut=(hux)x+q, where g, h and q are functions of x, subject to some general boundary conditions. By developing a maximum principle for the boundary value problem, rather than the equation, we prove the uniqueness of a nonnegative solution that depends continuously on boundary values.

scholarly journals On a Conjecture for the One-Dimensional Perturbed Gelfand Problem for the Combustion Theory

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2137
Author(s):  
Huizeng Qin ◽  
Youmin Lu
Keyword(s):  
Boundary Value Problem ◽  
Numerical Computation ◽  
Unique Solution ◽  
Boundary Value ◽  
Boundary Values ◽  
Three Solutions ◽  
One Dimensional ◽  
The One ◽  
Gelfand Problem ◽  
Existing Result

We investigate the well-known one-dimensional perturbed Gelfand boundary value problem and approximate the values of α0,λ* and λ* such that this problem has a unique solution when 0<α<α0 and λ>0, and has three solutions when α>α0 and λ*<λ<λ*. The solutions of this problem are always even functions due to its symmetric boundary values and autonomous characteristics. We use numerical computation to show that 4.0686722336<α0<4.0686722344. This result improves the existing result for α0≈4.069 and increases the accuracy of α0 to 10−8. We developed an algorithm that reduces errors and increases efficiency in our computation. The interval of λ for this problem to have three solutions for given values of α is also computed with accuracy up to 10−14.

scholarly journals Functions with the One-dimensional Holomorphic Extension Property

2019 ◽  
pp. 439-443
Author(s):  
Simona G. Myslivets
Keyword(s):  
Extension Property ◽  
Holomorphic Extension ◽  
One Dimensional ◽  
Complex Lines ◽  
The One

In this paper we consider different families of complex lines, sufficient for holomorphic extension the functions f, defined on the boundary of a domain D Cn, n > 1, into this domain, and possessing the one-dimensional holomorphic extension property along this complex lines

scholarly journals Sign-Changing Solutions for the One-Dimensional Non-Local sinh-Poisson Equation

2020 ◽  
Vol 20 (4) ◽  
pp. 739-767
Author(s):  
Azahara DelaTorre ◽  
Gabriele Mancini ◽  
Angela Pistoia
Keyword(s):  
Poisson Equation ◽  
Blow Up ◽  
Galvanic Corrosion ◽  
Careful Analysis ◽  
Local Version ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Non Local ◽  
The One ◽  
Sign Changing Solutions

AbstractWe study the existence of sign-changing solutions for a non-local version of the sinh-Poisson equation on a bounded one-dimensional interval I, under Dirichlet conditions in the exterior of I. This model is strictly related to the mathematical description of galvanic corrosion phenomena for simple electrochemical systems. By means of the finite-dimensional Lyapunov–Schmidt reduction method, we construct bubbling families of solutions developing an arbitrarily prescribed number sign-alternating peaks. With a careful analysis of the limit profile of the solutions, we also show that the number of nodal regions coincides with the number of blow-up points.

Topographische Orientierung bei Patienten mit erworbener Hirnschädigung

1999 ◽  
Vol 10 (2) ◽  
pp. 77-86
Author(s):  
Martina Kindsmüller ◽  
Andrea Kaindl ◽  
Uwe Schuri ◽  
Alf Zimmer
Keyword(s):  
Brain Damage ◽  
Cognitive Deficits ◽  
Hospital Setting ◽  
Hospital Staff ◽  
Reading Test ◽  
Map Reading ◽  
Several Variables ◽  
Topographical Orientation ◽  
The One ◽  
Behavioral Memory

Topographical Orientation in Patients with Acquired Brain Damage Abstract: A study was conducted to investigate the abilities of topographical orientation in patients with acquired brain damage. The first study investigates the correlation between wayfinding in a hospital setting and various sensory and cognitive deficits as well as the predictability of navigating performance by specific tests, self-rating of orientation ability and rating by staff. The investigation included 35 neuropsychological patients as well as 9 control subjects. Several variables predicted the wayfinding performance reasonably well: memory tests like the one introduced by Muramoto and a subtest of the Rivermead Behavioral Memory Test, the Map Reading Test and the rating by hospital staff. Patients with hemianopia experienced significant difficulty in the task.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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