Zobrazeno 1 - 10
of 149
pro vyhledávání: '"Rupert L. Frank"'
Publikováno v:
Mathematics in Engineering, Vol 2, Iss 1, Pp 119-140 (2020)
For dimensions $N \geq 4$, we consider the Br\'ezis-Nirenberg variational problem of finding \[ S(\epsilon V) := \inf_{0\not\equiv u\in H^1_0(\Omega)} \frac{\int_\Omega |\nabla u|^2\, dx +\epsilon \int_\Omega V\, |u|^2\, dx}{\left(\int_\Omega |u|^q \
Externí odkaz:
https://doaj.org/article/6d4356af011146a78be5d18d0a9e1839
Autor:
Rupert L. Frank, Simon Larson
Publikováno v:
Probability and Mathematical Physics. 3:431-490
We are interested in the nature of the spectrum of the one-dimensional Schr\"odinger operator $$ - \frac{d^2}{dx^2}-Fx + \sum_{n \in \mathbb{Z}}g_n \delta(x-n) \qquad\text{in } L^2(\mathbb{R}) $$ with $F>0$ and two different choices of the coupling c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f558d89da0750d86f3fb66011cbd0d7a
https://doi.org/10.2140/pmp.2022.3.431
https://doi.org/10.2140/pmp.2022.3.431
Publikováno v:
Density Functionals for Many-Particle Systems ISBN: 9789811272141
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8d0cd520043108e55bc0635e67b78318
https://doi.org/10.1142/9789811272158_0002
https://doi.org/10.1142/9789811272158_0002
Publikováno v:
Density Functionals for Many-Particle Systems ISBN: 9789811272141
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e44cc15f5215cbbeb18b9ddfc8bd82c7
https://doi.org/10.1142/9789811272158_0003
https://doi.org/10.1142/9789811272158_0003
The analysis of eigenvalues of Laplace and Schrödinger operators is an important and classical topic in mathematical physics with many applications. This book presents a thorough introduction to the area, suitable for masters and graduate students,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8f5b07d1fea6219f303aa90df5f1ece3
https://doi.org/10.1017/9781009218436
https://doi.org/10.1017/9781009218436
Autor:
Simon Larson, Rupert L. Frank
Publikováno v:
Functional Analysis and Its Applications. 55:174-177
Davies’ version of the Hardy inequality gives a lower bound for the Dirichlet integral of a function vanishing on the boundary of a domain in terms of the integral of the squared function with a weight containing the averaged distance to the bounda
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5e4ad00fc98d1df81e3029844dbdeca3
https://doi.org/10.1134/s0016266321020106
https://doi.org/10.1134/s0016266321020106
Publikováno v:
Proceedings of the American Mathematical Society. 149:265-278
We prove the non-degeneracy for the critical Lane–Emden system − Δ U = V p , − Δ V = U q , U , V > 0 in R N \begin{equation*} -\Delta U = V^p,\quad -\Delta V = U^q,\quad U, V > 0 \quad \text {in } \mathbb {R}^N \end{equation*} for all N ≥ 3
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5048db431657610f0337fd59a056d176
https://doi.org/10.1090/proc/15217
https://doi.org/10.1090/proc/15217
In dimension two, we investigate a free energy and the ground state energy of the Schrödinger–Poisson system coupled with a logarithmic nonlinearity in terms of underlying functional inequalities which take into account the scaling invariances of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8f166d8d897fae3056a326d3e1dd0684
https://resolver.caltech.edu/CaltechAUTHORS:20211018-185208122
https://resolver.caltech.edu/CaltechAUTHORS:20211018-185208122
Autor:
Elliott H. Lieb, Rupert L. Frank
Our recent work on the Burchard-Choksi-Topaloglu flocking problem showed that in the large mass regime the ground state density profile is the characteristic function of some set. Here we show that this set is, in fact, a round ball. The essential ma
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::683fec6a0e805b609d5369819b502377
https://resolver.caltech.edu/CaltechAUTHORS:20211201-160010515
https://resolver.caltech.edu/CaltechAUTHORS:20211201-160010515