- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 23:17:19
9
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=9&iss=5&update_since=2024-03-28
Zeitschrift für Analysis und ihre Anwendungen
Z. Anal. Anwend.
ZAA
0232-2064
1661-4534
Partial differential equations
Ordinary differential equations
Integral equations
Numerical analysis
10.4171/ZAA
http://www.ems-ph.org/doi/10.4171/ZAA
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2006)
9
1990
5
Iterated Dirac Operators in $\mathbb C^n$
John
Ryan
University of Arkansas, FAYETTEVILLE, UNITED STATES
We give a clssification of linear, conformally invariant, Clifford algebra valued differential operators over $\mathbb C^n$. Such operators comprise of the Dirac operator and its iterates. We show that the function theory, associated to the Dirac operator in $\mathbb R^n$ and $\mathbb C^n$ can be generalized to all these operators.
General
385
401
10.4171/ZAA/410
http://www.ems-ph.org/doi/10.4171/ZAA/410
Maximal Op*-Algebras on DF-Domains
Heinz
Junek
Universität Potsdam, POTSDAM, GERMANY
Let $D$ be any dense domain in a Hilbert space and let $\mathcal L^+ (D)$ be the maximaximal Op*-algebra of (possibly unbounded) linear operators. In this paper the uniform topology $\tau_D$ on $\mathcal L^+ (D)$ is investigated for the case where $D$ is a DF-space with respect to the graph topology. As a main result, a characterization of the bounded subsets of $D$ and of the topology $\tau_D$ by strongly bounded selfadjoint operators is given. Especially, each bounded subset of $D$ is contained in some bounded ellipsoid. This is applied to approximate the operators in $\mathcal L^+ (D)$ by bounded ones.
General
403
414
10.4171/ZAA/411
http://www.ems-ph.org/doi/10.4171/ZAA/411
Potential Flow Past a Circular Cylinder with Permeable Surface and Nonlinear Filtration Law
Elias
Wegert
Bergakademie Freiberg, FREIBERG, GERMANY
Lothar
von Wolfersdorf
Technische Universität, FREIBERG, GERMANY
The plane potential flow past a circular cylinder with porous surface for two classes of nonlinear filtration laws is dealt with by reducing the problem to a nonlinear singular integral equation and to a linear Riemann-Hilbert problem for a quasilinear equation of Beltrami type, respectively. A general topological existence theorem for the problem will be proven.
General
415
428
10.4171/ZAA/412
http://www.ems-ph.org/doi/10.4171/ZAA/412
Elliptic Oscillation Theory
Velmer
Headley
Brock University, ST. CATHARINES, CANADA
General
429
432
10.4171/ZAA/413
http://www.ems-ph.org/doi/10.4171/ZAA/413
Zur klassischen Kontaktaufgabe der Elastostatik
Lothar
Jentsch
Technische Universität Chemnitz-Zwickau, CHEMNITZ, GERMANY
For the study of boundary contact problems of thermoelastostatics, thermoelastic vibrations and other models with boundary integral methods the main difficulty which arises is, that displacement and stress contact conditions are to fulfil on the contact-surface between the elastic homogeneous parts. To solve these difficulties one is forced to study the contact problem of elastostatics. It is proved that an earlier potential representation is proper for getting some better results: 1. The boundary integral operator $\mathcal K$ of the contact problem is invertible without any assumption on the Poisson rations of the elastic parts. 2. $\mathcal K$ is a strongly elliptic pseudodifferential operator of order zero. Therefore theorems on asymptotic error estimates for boundary element methods are applicable.
General
433
453
10.4171/ZAA/414
http://www.ems-ph.org/doi/10.4171/ZAA/414
Zur Regularität einer Kontakt-Randwertaufgabe
Rainer
Schumann
, LEIPZIG, GERMANY
It is proved that the solution of a contact boundary value problem in linear $n$-dimensional elasticity belongs to $C^{1+\alpha}$ if the normal component of the displacement vector does.
General
455
465
10.4171/ZAA/415
http://www.ems-ph.org/doi/10.4171/ZAA/415
On the Singular Behaviour of Fluid in a Vertical Wedge
Erich
Miersemann
Universität Leipzig, LEIPZIG, GERMANY
Solutions of capillary surface equation over domains with corners are considered. It is assumed that the corner is bounded by curves which make an interior angle $2\alpha$ with $0 < 2\alpha < \pi$ and $\alpha + \gamma < \pi /2$, where $\gamma, 0 < \gamma > \pi /2$ is the contact angle between the surface and the container wall. An asymptotic formula for the solutions near the corner is given.
General
467
471
10.4171/ZAA/416
http://www.ems-ph.org/doi/10.4171/ZAA/416
Ein Fixpunktsatz für mehrdeutige konvexe Abbildungen auf der Sphäre
Herbert
Beckert
Universität Leipzig, LEIPZIG, GERMANY
The well-known fixed point theorem of Brouwer-Poincaré is generalized for upper semicontinuous multivalued mappings of the sphere $S^{n–1}$ ($n$ odd) on convex domains of $S^{n–1}$.
General
473
475
10.4171/ZAA/417
http://www.ems-ph.org/doi/10.4171/ZAA/417
Ein Fixpunktsatz für mehrdeutige nichtazyklische Abbildungen auf der Sphäre
Herbert
Beckert
Universität Leipzig, LEIPZIG, GERMANY
General
477
480
10.4171/ZAA/418
http://www.ems-ph.org/doi/10.4171/ZAA/418