%0 Journal Article %1 ISI:000372802900002 %A Barseghyan, Diana %A Exner, Pavel %A Kovarik, Hynek %A Weidl, Timo %C 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE %D 2016 %I WORLD SCIENTIFIC PUBL CO PTE LTD %J REVIEWS IN MATHEMATICAL PHYSICS %K Laplacian; bounds} discrete eigenvalue spectrum; {Magnetic %N 1 %R 10.1142/S0129055X16500021 %T Semiclassical bounds in magnetic bottles %V 28 %X The aim of the paper is to derive spectral estimates into several classes of magnetic systems. They include three-dimensional regions with Dirichlet boundary as well as a particle in R-3 confined by a local change of the magnetic field. We establish two-dimensional Berezin-Li-Yau and Lieb-Thirring-type bounds in the presence of magnetic fields and, using them, get three-dimensional estimates for the eigenvalue moments of the corresponding magnetic Laplacians.

@article{ISI:000372802900002, abstract = {{The aim of the paper is to derive spectral estimates into several classes of magnetic systems. They include three-dimensional regions with Dirichlet boundary as well as a particle in R-3 confined by a local change of the magnetic field. We establish two-dimensional Berezin-Li-Yau and Lieb-Thirring-type bounds in the presence of magnetic fields and, using them, get three-dimensional estimates for the eigenvalue moments of the corresponding magnetic Laplacians.}}, added-at = {2017-05-18T11:32:12.000+0200}, address = {{5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE}}, affiliation = {{Barseghyan, D; Exner, P (Reprint Author), Acad Sci Czech Republic, Inst Nucl Phys, Dept Theoret Phys, CZ-25068 Rez, Czech Republic. Barseghyan, D (Reprint Author), Univ Ostrava, Fac Sci, Dept Math, 30 Dubna 22, CZ-70103 Ostrava, Czech Republic. Exner, P (Reprint Author), Czech Tech Univ, Doppler Inst Math Phys \& Appl Math, Brehova 7, Prague 11519, Czech Republic. Kovarik, H (Reprint Author), Univ Brescia, Sez Matemat, Dicatam, Via Branze 38, I-25123 Brescia, Italy. Weidl, T (Reprint Author), Univ Stuttgart, Inst Anal Dynam \& Modellierung, Fak Math \& Phys, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Barseghyan, Diana; Exner, Pavel, Acad Sci Czech Republic, Inst Nucl Phys, Dept Theoret Phys, CZ-25068 Rez, Czech Republic. Barseghyan, Diana, Univ Ostrava, Fac Sci, Dept Math, 30 Dubna 22, CZ-70103 Ostrava, Czech Republic. Exner, Pavel, Czech Tech Univ, Doppler Inst Math Phys \& Appl Math, Brehova 7, Prague 11519, Czech Republic. Kovarik, Hynek, Univ Brescia, Sez Matemat, Dicatam, Via Branze 38, I-25123 Brescia, Italy. Weidl, Timo, Univ Stuttgart, Inst Anal Dynam \& Modellierung, Fak Math \& Phys, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.}}, article-number = {{1650002}}, author = {Barseghyan, Diana and Exner, Pavel and Kovarik, Hynek and Weidl, Timo}, author-email = {{dianabar@ujf.cas.cz exner@ujf.cas.cz hynek.kovarik@unibs.it weidl@mathematik.uni-stuttgart.de}}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/210c4308b8b87e7bdea79b62aa1516ab9/hermann}, doi = {{10.1142/S0129055X16500021}}, eissn = {{1793-6659}}, funding-acknowledgement = {{Czech Science Foundation (GACR) {[}14-06818S]; University of Ostrava; project ``Support of Research in the Moravian-Silesian Region{''}; Gruppo Nazionale per Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM); MIUR-PRIN; DFG {[}WE 1964/4-1, GRK 1838]}}, funding-text = {{The research was supported by the Czech Science Foundation (GACR) within the project 14-06818S. D.B. acknowledges the support of the University of Ostrava and the project ``Support of Research in the Moravian-Silesian Region 2013{''}. H.K. was supported by the Gruppo Nazionale per Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The support of MIUR-PRIN2010-11 grant for the project ``Calcolo delle variazioni{''} (H.K.) is also gratefully acknowledged. T.W. was in part supported by the DFG project WE 1964/4-1 and the DFG GRK 1838.}}, interhash = {ec89490965296006eb92fd562de5995f}, intrahash = {10c4308b8b87e7bdea79b62aa1516ab9}, issn = {{0129-055X}}, journal = {{REVIEWS IN MATHEMATICAL PHYSICS}}, keywords = {Laplacian; bounds} discrete eigenvalue spectrum; {Magnetic}, keywords-plus = {{LIEB-THIRRING INEQUALITIES; SCHRODINGER-OPERATORS; ASYMPTOTICS; EIGENVALUES; DIRICHLET; BEHAVIOR; DOMAINS}}, language = {{English}}, month = {{FEB}}, number = {{1}}, number-of-cited-references = {{22}}, orcid-numbers = {{Kovarik, Hynek/0000-0003-3647-8447}}, publisher = {{WORLD SCIENTIFIC PUBL CO PTE LTD}}, research-areas = {{Physics}}, researcherid-numbers = {{Kovarik, Hynek/K-9521-2015}}, times-cited = {{0}}, timestamp = {2017-05-18T09:32:12.000+0200}, title = {{Semiclassical bounds in magnetic bottles}}, type = {{Review}}, volume = {{28}}, web-of-science-categories = {{Physics, Mathematical}}, year = {{2016}} }