- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 12:46:12
17
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=21&iss=1&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)
21
2002
1
Tensor Algebras and Displacement Structure I. The Schur Algorithm
Tiberiu
Constantinescu
University of Texas at Dallas, RICHARDSON, UNITED STATES
J.
Johnson
University of Texas at Dallas, RICHARDSON, UNITED STATES
Displacement structure, tensor algebras, Schur algorithm
In this paper we explore the connection between tensor algebras and displacement structure. Thus, we describe a scattering experiment in this framework, we obtain a realization of the elements of the tensor algebra as transfer maps of a certain class of non-stationary linear systems, and we describe a Schur type algortihm for the Schur elements of the tensor algebra.
Linear and multilinear algebra; matrix theory
Operator theory
General
3
20
10.4171/ZAA/1062
http://www.ems-ph.org/doi/10.4171/ZAA/1062
Quaternionic Reformulation of Maxwell Equations for Inhomogeneous Media and New Solutions
Vladislav
Kravchenko
Cinvestav del IPN - Querétaro, SANTIAGO DE QUERÉTARO, MEXICO
Inhomogeneous media, quaternionic analysis, Maxwell equations
We propose a simple quaternionic reformulation of Maxwell equations for inhomogeneous media and use it in order to obtain new solutions in a static case.
Functions of a complex variable
Optics, electromagnetic theory
General
21
26
10.4171/ZAA/1063
http://www.ems-ph.org/doi/10.4171/ZAA/1063
Special First Order Systems in Clifford Analysis and Resolutions
Irene
Sabadini
Politecnico di Milano, MILANO, ITALY
Franciscus
Sommen
Universiteit Gent, GENT, BELGIUM
Abstract vector variables, monogenic functions of higher spin, matrix variables, combinatorial systems, resolutions, syzygies
In this paper we present and discuss to some extent a number of first order systems of partial differential operators with constant coefficients which arise naturally within the language of Clifford analysis. We also present resolutions for certain examples.
Linear and multilinear algebra; matrix theory
Functions of a complex variable
Partial differential equations
General
27
55
10.4171/ZAA/1064
http://www.ems-ph.org/doi/10.4171/ZAA/1064
Quasilinear Elliptic Systems of Second Order in Domains with Corners and Edges: Nemytskij Operator, Local Existence and Asymptotic Behaviour
Felix
Ali Mehmeti
Université de Valenciennes et du Hainaut Cambrésis, VALENCIENNES CEDEX 9, FRANCE
M.
Bochniak
Universität Ulm, ULM, GERMANY
Serge
Nicaise
Université de Valenciennes et du Hainaut Cambrésis, VALENCIENNES CEDEX 9, FRANCE
Anna-Margarete
Sändig
Universität Stuttgart, STUTTGART, GERMANY
Quasilinear elliptic problems, weighted Sobolev spaces with attached asymptotics, asymptotic behaviour near conical points and edges, Nemytskij operators, multiplication theorems
We consider systems of quasilinear partial differential equations of second order in two- and three-dimensional domains with corners and edges. The analysis is performed in weighted Sobolev spaces with attached asymptotics generated by the asymptotic behaviour of the solutions of the corresponding linearized problems near boundary singularities. Applying the Local Invertibility Theorem in these spaces we find conditions which guarantee existence of small solutions of the nonlinear problem having the same asymptotic behaviour as the solutions of the linearized problem. The main tools are multiplication theorems and properties of composition (Nemytskij) operators in weighted Sobolev spaces. As application of the general results a steady-state drift-diffusion system is explained.
Partial differential equations
Operator theory
General
57
90
10.4171/ZAA/1065
http://www.ems-ph.org/doi/10.4171/ZAA/1065
Local Existence Result of the Dopant Diffusion in Arbitrary Space Dimensions
R.
Bader
Technische Universität München, MÜNCHEN GARCHING, GERMANY
W.
Merz
Technische Universität München, MÜNCHEN GARCHING, GERMANY
Dopant diffusion, nonlinear reaction-drift-diffusion equations, ordinary differential equations in Banach spaces
In this paper we consider the pair diffusion process in more than two spatial dimensions. In this case we are able to prove just a local existence result, since it is not possible to deduce global a priori estimates for the equations as it can be done in the two-dimensional case. The model includes a nonlinear system of reaction-drift-diffusion equations, a nonlinear ordinary differential equation in Banach spaces and an elliptic equation for the electrostatic potential. The local existence result is based on the fixed point theorem of Schauder.
Ordinary differential equations
Partial differential equations
General
91
111
10.4171/ZAA/1066
http://www.ems-ph.org/doi/10.4171/ZAA/1066
A Transmission Problem with a Fractal Interface
Maria Rosaria
Lancia
Università di Roma La Sapienza, ROMA, ITALY
Fractal boundaries, Dirichlet forms, transmission problems
In this paper we study a transmission problem with a fractal interface $K$, where a second order transmission condition is imposed. We consider the case in which the interface $K$ is the Koch curve and we prove existence and uniqueness of the weak solution of the problem in $V (\Omega, K)$, a suitable ”energy space”. The link between the variational formulation and the problem is possible once we recover a version of the Gauss-Green formula for fractal boundaries, hence a definition of ”normal derivative”.
Potential theory
Partial differential equations
Measure and integration
Optics, electromagnetic theory
113
133
10.4171/ZAA/1067
http://www.ems-ph.org/doi/10.4171/ZAA/1067
Sobolev and Morrey Estimates for Non-Smooth Vector Fields of Step Two
A.
Montanari
Università di Bologna, BOLOGNA, ITALY
Daniele
Morbidelli
Università di Bologna, BOLOGNA, ITALY
Sobolev inequalities, Freezing method, homogeneous spaces
We prove Sobolev-type and Morrey-type inequalities for Sobolev spaces related to a family of non-smooth vector fields which formally satisfy the Hörmander condition of step 2. The coefficients of the vector fields are not regular enough to define the Carnot-Carathéodory distance. Thus the result is proved by developing a real analysis technique which is based on an approximation procedure of Lipschitz continuous vector fields with a family of left-invariant first order operators on a nilpotent Lie group.
Functional analysis
General
135
157
10.4171/ZAA/1068
http://www.ems-ph.org/doi/10.4171/ZAA/1068
$L_q-L_r$-Estimates for Non-Stationary Stokes Equations in an Aperture Domain
Helmut
Abels
Universität Regensburg, REGENSBURG, GERMANY
Stokes equations, aperture domains, asymptotic behavior, asymptotic expansions
This article deals with asymptotic estimates of strong solutions of Stokes equations in aperture domains. An aperture domain is a domain, which outside a bounded set is identical to two half spaces separated by a wall and connected inside the bounded set by one or more holes in the wall. It is known that the corresponding Stokes operator generates a bounded analytic semigroup in the closed subspace $J_q(\Omega)$ of divergence free vector fields of $L_q(\Omega)^n$. We deal with $L_q-L_r$-estimates for the semigroup, which are known for $\mathbb R^n$, the half space and exterior domains.
Partial differential equations
Fluid mechanics
General
159
178
10.4171/ZAA/1069
http://www.ems-ph.org/doi/10.4171/ZAA/1069
Some Embeddings into the Multiplier Spaces Associated to Besov and Lizorkin-Triebel Spaces
D.
Drihem
M'Sila University, M'SILA, TUNISIA
Madani
Moussai
Université de M'sila, M'SILA, ALGERIA
Besov spaces, Lizorkin-Triebel spaces, pointwise multipliers
We study the set of pointwise multipliers in the Lizorkin-Triebel space $F^{s,q}_p$ and of the corresponding multiplier set in the Besov space $B^{s,q}_p$, where we give sufficient conditions on the parameters $s$, $p$ and $p_1$ such that the embeddings $F^{n/p_1,\infty}_{p_1} \cap L^\infty \hookrightarrow M(F^{s,q}_p)$ and $B^{n/p_1, \infty}_{p_1} \hookrightarrow M(B^{s,q}_p)$ hold.
Functional analysis
General
179
184
10.4171/ZAA/1070
http://www.ems-ph.org/doi/10.4171/ZAA/1070
Asymptotics of Solutions for fully Nonlinear Elliptic Problems at Nearly Critical Growth
Alessandro
Musesti
Università Cattolica del Sacro Cuore, BRESCIA, ITALY
Marco
Squassina
Università degli Studi di Verona, VERONA, ITALY
Concentration-compactness principle, critical exponent, best Sobolev constant, fully nonlinear elliptic problems
In this paper we deal with the study of limits of solutions of a class of fully nonlinear elliptic problems at nearly critical growth. By means of P.L. Lions’ concentration-compactness principle, we prove an alternative result for the existence of non-trivial solutions of the limit problem.
Partial differential equations
General
185
201
10.4171/ZAA/1071
http://www.ems-ph.org/doi/10.4171/ZAA/1071
Stably Solvable Maps are Unstable under Small Perturbations
Massimo
Furi
Università di Firenze, FIRENZE, ITALY
Nonlinear spectral theory, stably solvable maps, nonlinear operators
We show that the set of stably solvable maps from an infinite dimensional Banach space $E$ into itself is not open in the topological space $C(E)$ of the continuous selfmaps of $E$. The question of whether or not this set is open is related to nonlinear spectral theory and was posed in [7].
Operator theory
General
203
208
10.4171/ZAA/1072
http://www.ems-ph.org/doi/10.4171/ZAA/1072
Solution Decompositions for Linear Convection-Diffusion Problems
Torsten
Linß
Technische Universität Dresden, DRESDEN, GERMANY
Convection-diffusion, singular perturbation, solution decomposition
We consider a singularly perturbed convection-diffusion problem. The existence of certain decompositions of the solution into a regular solution component and a layer component is studied. Such decompositions are useful for the convergence analysis of numerical methods. Our aim is to show that such decompositions exist under less restrictive assumptions on the data of the problem than those required in earlier publications.
Ordinary differential equations
General
209
214
10.4171/ZAA/1073
http://www.ems-ph.org/doi/10.4171/ZAA/1073
On the Optimality for Cascade Connection of Passive Scattering Systems and the Best Minorant Outer Function
Nguyen Minh
Hang
Ho Chi Minh City University of Technology, HO CHI MINH CITY, VIETNAM
Passive scattering system, optimality, controllability, best minorant outer function
In this paper we study passive scattering systems in the framework introduced by Arov. The main purpose is to find conditions for conserving the optimality of a cascade connection of passive scattering systems in terms of the best minorant outer function and to characterize optimal passive scattering systems which have the same transfer function.
Calculus of variations and optimal control; optimization
Systems theory; control
General
215
231
10.4171/ZAA/1074
http://www.ems-ph.org/doi/10.4171/ZAA/1074
Orienting Method for Obstacle Problems
Hoàng Xuân
Phú
Institute of Mathematics, HANOI, VIETNAM
T.D.
Long
Hue University, HUE, VIETNAM
Obstacle problems, variation problems, variational inequality, coincidence and non-coincidence set, orienting method
Operator theory
Partial differential equations
Calculus of variations and optimal control; optimization
General
233
248
10.4171/ZAA/1075
http://www.ems-ph.org/doi/10.4171/ZAA/1075
Global Existence for some Integro-Differential Equations with Delay Subject to Non-Local Conditions
S.
Mazouzi
University Badji Mokhtar, ANNABA, ALGERIA
Nasser-edine
Tatar
Dept. of Mathematics, DHAHRAN, SAUDI ARABIA
Nonlocal conditions, mild solutions, semigroups, Schaefer’s fixed point theorem, integro-differential equations
By making use of the Leray-Schauder fixed point theorem we prove the global existence of solutions to some integro-differential equations with delay subject to non-local conditions, and this problem is considered in an arbitrary Banach space.
Partial differential equations
General
249
256
10.4171/ZAA/1076
http://www.ems-ph.org/doi/10.4171/ZAA/1076
On the Hilbert Inequality With Weights
Gao
Mingzhe
Xiangxi Education College, HUNAN, CHINA
Wei
Shongrong
Zhaqing College, GUANGDONG, CHINA
He
Leping
Xiangxi Education College, HUNAN, CHINA
Hilbert inequality with weights, Hardy-Littlewood inequality, infimum, weight functions
In this paper, it is shown that a Hilbert-type inequality with weight $\omega(n) = \pi – \frac{\theta}{\sqrt{2n+1}}$ can be established where $\theta = \frac{17}{20}$. As application, a quite sharp result of the Hardy-Littlewood inequality is obtained and some further extensions are obtained.
Approximations and expansions
Real functions
General
257
263
10.4171/ZAA/1077
http://www.ems-ph.org/doi/10.4171/ZAA/1077
Die Nevanlinna-Charakteristik von algebroiden Funktionen und ihren Ableitungen
Tomohiko
Sato
Osaka University Graduate School of Engineering Sc, OSAKA, JAPAN
Growth of characteristic functions, meromorphic functions and their derivatives, algebroid functions (in complex analysis)
It is well known that, when $f(z)$ is an entire function of order $\rho$ and $\rho > \infty$, then the limit lim sup$_{r \rightarrow \infty} \frac{T(r,f')}{T(r,f)}$ is finite as $r \rightarrow \infty$ through all values or outside a set $E$ of finite measure. But for $\rho = \infty$, Hayman has shown that the assertion does not hold by constructing an entire function $f(z)$ and an exceptional set $E$ of even infinite measure. In this paper, we will further extend his result to the case where $f(z)$ is an algebroid function of order $\rho = \infty$.
General
265
272
10.4171/ZAA/1078
http://www.ems-ph.org/doi/10.4171/ZAA/1078