- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 06:09:33
7
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=3&iss=5&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)
3
1984
5
On Strongly Nonlinear Poincaré Boundary Value Problems for Harmonic Functions
Lothar
von Wolfersdorf
Technische Universität, FREIBERG, GERMANY
A class of strongly nonlinear Poincaré problems for harmonic functions in the unit disk is studied by reducing them to a new integral equation system to which Schauder’s fixed point theorem is applied. Specific existence results are given for several special cases, in particular the quasilinear case is dealt with in detail.
General
385
399
10.4171/ZAA/116
http://www.ems-ph.org/doi/10.4171/ZAA/116
Konforminvarianten vom Gewicht –1 elnes Zusammenhanges oder Eichfeldes
Rainer
Schimming
Ernst-Moritz-Arndt-Universität Greifswald, GREIFSWALD, GERMANY
A connection or a gauge field in a vector bundle over a riemannian manifold is introduced by means of some given Laplace-like operator. Applying new results of P. Günther and V. Wünsch we construct a sequence of conformal invariants of weight –1 for a gauge field. These are relevant e.g. in the theory of Huygens’ principle. We calculate the relative conformal invariants for some examples; especially they vanish for any instanton gauge field.
General
401
412
10.4171/ZAA/117
http://www.ems-ph.org/doi/10.4171/ZAA/117
Ein Randwertproblem für eine nichtlineare Gleichung gemischtenTyps im $\mathbb R^3$
Andreas
Müller-Rettkowski
Karlsruhe Institute of Technology (KIT), KARLSRUHE, GERMANY
A boundary value problem for the equation $Tu = Lu — u |u|^p = f(x, u), p > 0$, is studied in a simply connected bounded domain $G$ of $\mathbb R^3$. Here $L$ denotes a linear second order differential operator which is elliptic, parabolic or hyperbolic if $x_3 > 0, x_3 = 0$ or $x_3 < 0$, respectively. The boundary of 0 is formed by a non-characteristic and by two characteristic surfaces. The boundary value problem to be solved is to find a solution of the equation in 0 which assumes zero data on the non-characteristic and on one of the characteristic boundary surfaces. It is proved that this problem has a generalized solution belonging to $L^{p+2}$ and to a Sobolew space with weight. Using apriori estimates the solubility of a sequence of approximate problems is shown whose solutions turn out to converge towards a solution of the boundary value problem in question.
General
413
423
10.4171/ZAA/118
http://www.ems-ph.org/doi/10.4171/ZAA/118
On an Evolution Equation for a Non-Hypoelliptic Linear Partial Differential Operator from Stochastics
Karl
Doppel
Freie Universität Berlin, BERLIN, GERMANY
Niels
Jacob
University of Wales Swansea, SWANSEA, UNITED KINGDOM
Recently E. B. Dynkin [2] introduced and studied a non-hypoelliptic linear partial differential operator of even order (with constant coefficients) which originates from the theory of multi-parametric stochastic processes. Motivated by the consideiations of Dynkin the authors have solved a generalized Dirichlet problem for this differential operator in their work [1]. Our aim in the present paper is to investigate the Cauchy problem for the corresponding evolution equation (in the time variable of first order); such a Cauchy problem could have applications to some questions from the stochastics.
General
425
433
10.4171/ZAA/119
http://www.ems-ph.org/doi/10.4171/ZAA/119
Einige Bemerkungen über die Fortsetzung positiv definiter Funktionen
Zoltán
Sasvári
Technische Universität Dresden, DRESDEN, GERMANY
In this note we give some extensions of continuous, positive definite functions on $(–a, a), 0 < a < \infty$. Theorem 3 yields as a special case a result of P. Lévy on periodic extensions.
General
435
440
10.4171/ZAA/120
http://www.ems-ph.org/doi/10.4171/ZAA/120
Three-dimensional dynamic problems of the nonclassical theory of thermoelasticity (in Russian)
Tengiz
Burchuladze
Georgian Acadademy of Sciences, TBILISI, GEORGIA
The paper deals with the dynamical differential equations of nonclassical thermoelasticity initiated by Green and Lindsay, which are characterized by using of two different relaxation times for describing the finite velocity of heat flux. Uniqueness theorems are proved by the aid of integral formulas. Some remarks are made on the applicability of potential methods to the study of the related initial boundary value problems.
General
441
455
10.4171/ZAA/121
http://www.ems-ph.org/doi/10.4171/ZAA/121
Einige Bemerkungen zur Anfangs-Randwertaufgabe $\frac{\partial}{\partial t} u - h(x, t) \Delta u =f$ mit meßbarem Koeffizienten
Jörg
Heinrich
Technische Universität Dresden, DRESDEN, GERMANY
In the present paper the mixed problem $\frac{\partial}{\partial t} u - h(x, t) \Delta u =f$ with measurable coefficient is considered at first for special domains (cubes) by a modification of Banach’s fixed point theorem. Starting from this we get an existence and uniqueness theorem for domains of the class $O^2$. Several properties of the solution are discussed.
General
457
479
10.4171/ZAA/122
http://www.ems-ph.org/doi/10.4171/ZAA/122