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pro vyhledávání: '"46N20"'
We study Schr\"odinger operators $H:= -\Delta + V$ with potentials $V$ that have power-law growth (not necessarily polynomial) at 0 and at $\infty$ using methods of Lie theory (Lie-Rinehart algebras) and microlocal analysis. More precisely, we show t
Externí odkaz:
http://arxiv.org/abs/2412.19290
Autor:
Morrow, Bryce
In this paper, we present a concise development of the well-studied theory of trace class operators on infinite dimensional (separable) Hilbert spaces suitable for an advanced undergraduate, as well as a construction of the inverse Laplacian on close
Externí odkaz:
http://arxiv.org/abs/2411.17890
We introduce and analyse a class of weighted Sobolev spaces with mixed weights on angular domains. The weights are based on both the distance to the boundary and the distance to the one vertex of the domain. Moreover, we show how the regularity of th
Externí odkaz:
http://arxiv.org/abs/2409.18615
We study the asymptotic error between the finite element solutions of nonlocal models with a bounded interaction neighborhood and the exact solution of the limiting local model. The limit corresponds to the case when the horizon parameter, the radius
Externí odkaz:
http://arxiv.org/abs/2409.09270
Autor:
Hanche-Olsen, Harald, Holden, Helge
Publikováno v:
Published in Pure and Applied Functional Analysis, Volume 9, No 5, pp. 1133-1144 (2024)
A fundamental issue in the theory of time-dependent differential equations is to characterize precompact sets in Bochner spaces. We here survey the theory, starting with the classical Aubin-Lions inequality and its important extension by Dubinskii. I
Externí odkaz:
http://arxiv.org/abs/2402.07308
Autor:
Jaramillo, Gabriela
We prove existence of spiral waves in oscillatory media with nonlocal coupling. Our starting point is a nonlocal complex Ginzburg-Landau (cGL) equation, rigorously derived as an amplitude equation for integro-differential equations undergoing a Hopf
Externí odkaz:
http://arxiv.org/abs/2401.15226
Autor:
Kryspin, Marek, Mierczyński, Janusz
Publikováno v:
Journal of Differential Equations 409 (2024), 532-591
Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on the zero o
Externí odkaz:
http://arxiv.org/abs/2401.12328
Autor:
Mukherjee, Subhasish, Tice, Ian
We introduce a scale of anisotropic Sobolev spaces defined through a three-parameter family of Fourier multipliers and study their functional analytic properties. These spaces arise naturally in PDE when studying traveling wave solutions, and we give
Externí odkaz:
http://arxiv.org/abs/2312.06044
Motivated by the study of layer potentials on manifolds with straight conical or cylindrical ends, we introduce and study two classes (or calculi) of pseudodifferential operators defined on manifolds with cylindrical ends: the class of pseudodifferen
Externí odkaz:
http://arxiv.org/abs/2308.06308
We provide Fredholm conditions for compatible differential operators on certain Lie manifolds (that is, on certain possibly non-compact manifolds with nice ends). We discuss in more detail the case of manifolds with cylindrical, hyperbolic, and Eucli
Externí odkaz:
http://arxiv.org/abs/2308.06225