- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 09:13:46
7
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=35&iss=2&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)
35
2016
2
Mixed Norms and Iterated Rearrangements
Viktor
Kolyada
Karlstad University, KARLSTAD, SWEDEN
Javier
Soria
Universitat de Barcelona, BARCELONA, SPAIN
Rearrangements, embeddings, mixed norms, Lorentz spaces
We prove sharp estimates, and nd the optimal range of indices, for the comparison of mixed norms for both functions and their iterated rearrangements.
Functional analysis
Fourier analysis
119
138
10.4171/ZAA/1557
http://www.ems-ph.org/doi/10.4171/ZAA/1557
Sobolev Embedding Theorem for Irregular Domains and Discontinuity of $p \to p^*(p,n)$
Tomáš
Roskovec
Charles University, PRAGUE 8, CZECH REPUBLIC
Sobolev space, Sobolev embedding
For a domain $\Omega\subset\mathbb{R}^n$ we denote $$\begin{aligned}q_{\Omega}(p):=\operatorname{sup}\big\{r\in[1,\infty];\text{ for all } f:\Omega\rightarrow\mathbb{R}:(f\in W^{1,p}(\Omega)\Rightarrow f\in L^{r}(\Omega))\big\}. \end{aligned}$$ Let $p_0 \!\in \! [2,\infty).$ We construct a domain $\Omega \! \subset \! \mathbb{R}^2$ such that $q_{\Omega}(p)$ is discontinuous at $p_0.$
Functional analysis
139
152
10.4171/ZAA/1558
http://www.ems-ph.org/doi/10.4171/ZAA/1558
Parabolic Obstacle Problem with Measurable Data in Generalized Morrey Spaces
Sun-Sig
Byun
Seoul National University, SEOUL, SOUTH KOREA
Lubomira
Softova
Seconda Università degli Studi di Napoli , AVERSA, ITALY
Parabolic obstacle problem, generalized Morrey spaces, measurable coefficients, small BMO, Reifenberg flat domain
We study the global regularity in generalized Morrey spaces of the solutions to variational inequality and obstacle problem related to divergence form parabolic operator in bounded non-smooth domain. We impose minimal regularity conditions as to the coeffi cients of the operator so also to the boundary of the domain.
Partial differential equations
Functional analysis
153
171
10.4171/ZAA/1559
http://www.ems-ph.org/doi/10.4171/ZAA/1559
The Profile of Blow-Up for a Neumann Problem of Nonlocal Nonlinear Diffusion Equation with Reaction
Rong-Nian
Wang
Shanghai Normal University, SHANGHAI, CHINA
Zhi-Xue
Liu
Nanchang University, NANCHANG, CHINA
Yong
Zhou
Xiangtan University, XIANGTAN, HUNAN, CHINA
Nonlocal nonlinear diffusion, blow-up rate, blow-up set
In this note, we consider a Neumann problem for nonlocal nonlinear diffusion equation with reaction, which may be seen as a significant generalization of the usual Neumann problem for the heat equation. For the blow-up solutions, the blow-up rate estimates and spacial localization of blow-up set are studied.
Partial differential equations
Functional analysis
173
180
10.4171/ZAA/1560
http://www.ems-ph.org/doi/10.4171/ZAA/1560
An Existence Result for Fractional Kirchhoff-Type Equations
Giovanni
Molica Bisci
Università degli Studi Mediterranea de Reggio Calabria, REGGIO CALABRIA, ITALY
Francesco
Tulone
Università degli Studi di Palermo, PALERMO, ITALY
Fractional equations, variational methods, critical point results
The aim of this paper is to study a class of nonlocal fractional Laplacian equations of Kirchho ff-type. More precisely, by using an appropriate analytical context on fractional Sobolev spaces, we establish the existence of one non-trivial weak solution for nonlocal fractional problems exploiting suitable variational methods.
Partial differential equations
Operator theory
181
197
10.4171/ZAA/1561
http://www.ems-ph.org/doi/10.4171/ZAA/1561
An Example of a Non-Trivial, Non-Self-Adjoint Huygens Differential Equation in Four Independent Variables
Stephanie
Czapor
Laurential University, SUDBURY, ONTARIO, CANADA
Raymond
McLenaghan
University of Waterloo, WATERLOO, ONTARIO, CANADA
Initial value problem, Huygens' principle, Hadamard's problem, non-self-adjoint wave equation
A family of non-trivial, essentially non-self-adjoint wave equations which satisfy Huygens' principle is given. It is constructed on a 4-dimensional Lorentzian space which is a product of two 2-dimensional spaces of constant curvature. Prior to this example, the only known non-trivial Huygens equation was the scalar wave equation on the exact plane wave spacetime as presented by Günther.
Partial differential equations
Global analysis, analysis on manifolds
199
210
10.4171/ZAA/1562
http://www.ems-ph.org/doi/10.4171/ZAA/1562
A Rigorous Interpretation of Approximate Computations of Embedded Eigenfrequencies of Water Waves
Sergei
Nazarov
Institute for Problems in Mechanical Engineering RAS, ST. PETERSBURG, RUSSIAN FEDERATION
Keijo
Ruotsalainen
University of Oulu, OULU, FINLAND
Water waves, approximate computation of embedded eigenvalues, augmented scattering matrix, asymptotic analysis, perturbation techniques
In this paper, we will investigate embedded eigenvalues in the framework of the linearized theory of water waves. We assume that an approximation of an embedded eigenvalue is provided. To the question, whether there is a trapped mode near the computed solution, we provide an affirmative answer. We will prove that, under certain assumptions on the data for a water wave problem in an infinite channel $\Omega^0$, the result $\lambda^{0}$ of the numerical computation can be justified as follows: if the computational error $\varepsilon$ is sufficiently small, there exists a water domain $\Omega^\varepsilon$ which is a local regular perturbation of $\Omega^0$ and has an eigenvalue $\lambda^\varepsilon \in [\lambda^0 - c \varepsilon,\, \lambda^0 + c\varepsilon]$ embedded in the continuous spectrum. This conclusion is made by means of an asymptotic analysis of the augmented scattering matrix, whose properties guarantee a sufficient condition for the existence of trapped mode.
Mechanics of deformable solids
Fluid mechanics
211
242
10.4171/ZAA/1563
http://www.ems-ph.org/doi/10.4171/ZAA/1563