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pro vyhledávání: '"Ohtsuka, Hiroshi"'
We study a variational problem on $H^1({\mathbb R})$ under an $L^\infty$-constraint related to Sobolev-type inequalities for a class of generalized potentials, including $L^p$-potentials, non-positive potentials, and signed Radon measures. We establi
Externí odkaz:
http://arxiv.org/abs/2405.00730
We present a new method to determine the best constant of the Sobolev-type embedding in one dimension with a norm including a bounded inhomogeneous potential term. This problem is closely connected to the Green function of the Schr\"odinger operator
Externí odkaz:
http://arxiv.org/abs/2311.00708
Autor:
Ohtsuka, Hiroshi, Sato, Tomohiko
We determine the second term of the asymptotic expansions for the first m eigenvalues and eigenfunctions of the linearized Liouville-Gel'fand problem associated to solutions which blow-up at m points. Our problem is the case with an inhomogeneous coe
Externí odkaz:
http://arxiv.org/abs/2308.04157
Akademický článek
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We derive a second order estimate for the first m eigenvalues and eigenfunctions of the linearized Gel'fand problem associated to solutions which blow-up at m points. This allows us to determine, in some suitable situations, some qualitative properti
Externí odkaz:
http://arxiv.org/abs/1308.3628
Blow-up solutions to the two-dimensional Gel'fand problem are studied. It is known that the location of the blow-up points of these solutions is related to a Hamiltonian function involving the Green function of the domain. We show that this implies a
Externí odkaz:
http://arxiv.org/abs/1210.1373
Akademický článek
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Publikováno v:
In Journal of Mathematical Analysis and Applications 15 February 2013 398(2):692-706
Autor:
Ohtsuka, Hiroshi
Publikováno v:
数理解析研究所講究録別冊. :67-85
Motivated by several experimental facts, we are interested in the linear response of equilibrium vortices. In order to study the phenomenon, here we investigate the mean field limit of equilibrium vortices perturbed by an external field and derive th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=jairo_______::ac3c01307416cb14a19e63f2b651ff00
http://hdl.handle.net/2433/260678
http://hdl.handle.net/2433/260678
Publikováno v:
In Journal of Differential Equations 2010 249(6):1436-1465