- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 02:56:26
9
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=1&iss=4&update_since=2024-03-29
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)
1
1982
4
On some parabolic boundary control problems with constraints on the control and functional-constraints on the state
Fredi
Tröltzsch
Technische Universität Berlin, BERLIN, GERMANY
In this paper parabolic boundary control problems in a $n$-dimensional bounded domain are investigated, where in addition to a pointwise constraint on the control finitely many linear functional constraints on the state are given. As performance functional the $L_{\infty}$- or $L_2$-norm of the difference between the final state and a given (desired) state is used. A generalized bang-bang-principle is proved which expresses that under natural assumptions almost everywhere (with respect to the time) either the optimal control or the corresponding state is acting on the boundary of its constraints. The assumptions are discussed by examples.
General
1
13
10.4171/ZAA/23
http://www.ems-ph.org/doi/10.4171/ZAA/23
Starke Dualität bei verallgemeinerten Steuerproblemen
Sabine
Pickenhain
Brandenburgische Technische Universität Cottbus, COTTBUS, GERMANY
In this paper a generalized parametric variational problem with restrictions on the state domain and the control is considered and its dual problem constructed. Under weak assumptions, strong duality is shown between the primary and the dual problem.
General
15
24
10.4171/ZAA/24
http://www.ems-ph.org/doi/10.4171/ZAA/24
Differentiationsalgebren mit einem kubischen Element
Lothar
Berg
Universität Rostock, ROSTOCK, GERMANY
There are shown new possibilities for the multiplication of some distributions, namely, by means of matrix representations we prove the existence of nontrivial associative differential algebras with an element $h$ satisfying the cubic equation $2h^3 - 3h^2 + h = 0$, which can be interpreted as Heaviside’s jump function. One of these algebras is extended by adjunction of an integral of $h$.
General
25
30
10.4171/ZAA/25
http://www.ems-ph.org/doi/10.4171/ZAA/25
Über zufällige Störungen einer Basis aus Exponentialfunktionen im Raum $L_2 [-\pi, \pi]$
Klaus-Detlef
Kürsten
Universität Leipzig, LEIPZIG, GERMANY
We investigate the limit case $|s_n| = 1/4$ for the theorem of Paley and Wiener and some later authors on the basis properties of the perturbed system {exp $(i(n + s_n) t): n \in \mathbb Z$} in the space $L_2[-\pi, \pi]$. We prove that the perturbed system almost sure is no Riesz basis, if {$s_n$} is taken from $[- 1/4, 1/4]^{\mathbb Z}$ equipped with natural product measures.
General
31
36
10.4171/ZAA/26
http://www.ems-ph.org/doi/10.4171/ZAA/26
Factorization of operators mapping (F)-spaces into (DF)-spaces
Heinz
Junek
Universität Potsdam, POTSDAM, GERMANY
This paper deals with the factorization of linear operators mapping (F)-spaces into (DF)-spaces through Banach spaces and through operators of given operator ideals. Roughly speaking, we answer the question of, to what extend global properties of such operators are determined by their behaviour on the hounded subsets. The results are used to characterize the geometric structure of the neighbourhoods of zero in (F)-spaces by the geometry of their bounded sub-sets. Moreover, they allow further insights into the theory of nuclear (F)-spaces.
General
37
45
10.4171/ZAA/27
http://www.ems-ph.org/doi/10.4171/ZAA/27
Dualität bei Steuerungsproblemen und zugeordneten Flussproblemen I
Rolf
Klötzler
, BORSDORF, GERMANY
In this paper novel classes of relaxed problems are stated which are called flow problems. They are related to standard problems of optimal control with functions of one independent variable. Both of these optimization problems have in each case the same dual problem. However for flow problems one can prove the validity of strong duality under weaker assumptions.
General
47
57
10.4171/ZAA/28
http://www.ems-ph.org/doi/10.4171/ZAA/28
Zur Regularität verallgemeinerter Lösungen von quasilinearen elliptischen Differentialgleichungen zweiter Ordnung in Gebieten mit Ecken
Erich
Miersemann
Universität Leipzig, LEIPZIG, GERMANY
There are studied regularity properties of a class of quasilinear elliptic equations of second order in two-dimensional domains with corners. As an application of these, there is considered the minimal surface problem.
General
59
71
10.4171/ZAA/29
http://www.ems-ph.org/doi/10.4171/ZAA/29
The Galerkin approximation for quasilinear elliptic equations with rapidly (or slowly) increasing coefficients
Rainer
Schumann
, LEIPZIG, GERMANY
In this paper the convergence of Galerkin’s method is proved for quasilinear elliptic partial differential equations with rapidly (or slowly) increasing coefficients. The investigations are based on Gossez’s theory of pseudomonotone operators in complementary systems of Sobolev-Orlicz spaces.
General
73
85
10.4171/ZAA/30
http://www.ems-ph.org/doi/10.4171/ZAA/30
On a Class of Generalized $K$-Entropies and Bernoulli Shifts
Thomas
de Paly
Universität Leipzig, LEIPZIG, GERMANY
The paper presents the construction of an example important for the discussion of some generalizations of the $K$-entropy. These generalizations have been introduced in a previous paper. A formula for the generalized entropies of a process is calculated for the case where the process is given by a Bernoulli shift and a partition consisting only of cylinder sets. Furthermore, a special optimization problem on the set of all probability vectors of a given entropy is solved using a new method. The results of these computations are combined to the cited example.
General
87
96
10.4171/ZAA/31
http://www.ems-ph.org/doi/10.4171/ZAA/31