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pro vyhledávání: '"47H30"'
In this paper, we review the construction of periodic fundamental solutions and periodic layer potentials for various differential operators. Specifically, we focus on the Laplace equation, the Helmholtz equation, the Lam\'e system, and the heat equa
Externí odkaz:
http://arxiv.org/abs/2412.13001
Autor:
Bugajewski, Dawid
In this article, we study the properties of the autonomous superposition operator on the space of formal power series, including those with nonzero constant term. We prove its continuity and smoothness with respect to the topology of pointwise conver
Externí odkaz:
http://arxiv.org/abs/2409.09853
A global approximation method of Nystr\"om type is explored for the numerical solution of a class of nonlinear integral equations of the second kind. The cases of smooth and weakly singular kernels are both considered. In the first occurrence, the me
Externí odkaz:
http://arxiv.org/abs/2407.10842
Autor:
Molinarolo, Riccardo
In this paper we study the existence of solutions in parabolic Schauder space of a nonlinear mixed boundary value problem for the heat equation in a perforated domain. From a given regular open set $\Omega\subseteq\mathbb{R}^n$ we remove a cavity $\o
Externí odkaz:
http://arxiv.org/abs/2406.18315
We consider the heat equation in a domain that has a hole in its interior. We impose a Neumann condition on the exterior boundary and a nonlinear Robin condition on the boundary of the hole. The shape of the hole is determined by a suitable diffeomor
Externí odkaz:
http://arxiv.org/abs/2406.11365
In this paper, we completely give the solution of the problem of Littlewood-type randomization in the Hardy and Bergman spaces of Dirichlet series. The Littlewood-type theorem for Bergman spaces of Dirichlet series is very different from the correspo
Externí odkaz:
http://arxiv.org/abs/2402.00314
Publikováno v:
Mediterr. J. Math. 21, 149 (2024)
By means of fixed point index theory for multi-valued maps, we provide an analogue of the classical Birkhoff--Kellogg Theorem in the context of discontinuous operators acting on affine wedges in Banach spaces. Our theory is fairly general and can be
Externí odkaz:
http://arxiv.org/abs/2401.16050
Autor:
Niu Yeli, Wang Heping
Publikováno v:
Demonstratio Mathematica, Vol 57, Iss 1, Pp 1205-1213 (2024)
Let ff be a function defined on the real line, and Tf{T}_{f} be the corresponding superposition operator which maps hh to Tf(h){T}_{f}\left(h), i.e., Tf(h)=f∘h{T}_{f}\left(h)=f\circ h. In this article, the sufficient and necessary conditions such t
Externí odkaz:
https://doaj.org/article/90566d2c61934ee28460a595809a0137
This paper is divided into three parts. The first part focuses on periodic layer heat potentials, demonstrating their smooth dependence on regular perturbations of the support of integration. In the second part, we present an application of the resul
Externí odkaz:
http://arxiv.org/abs/2309.07501
Autor:
Drihem, Douadi
The aim of this paper is to present some necessary conditions for the boundedness of the mapping $f\mapsto |f|^{\mu },\mu >0$ on Besov spaces equipped with power weights.
Externí odkaz:
http://arxiv.org/abs/2305.14866