Geometric Control of the Robin Laplacian Eigenvalues: The Case of Negative Boundary Parameter
This paper is motivated by the study of the existence of optimal domains maximizing the k th Robin Laplacian eigenvalue among sets of prescribed measure, in the case of a negative boundary parameter. We answer positively to this question and prove an existence result in the class of measurable sets...
Gespeichert in:
| Veröffentlicht in: | The Journal of Geometric Analysis 2020-12, Vol.30 (4), p.4356-4385 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 4385 |
|---|---|
| container_issue | 4 |
| container_start_page | 4356 |
| container_title | The Journal of Geometric Analysis |
| container_volume | 30 |
| creator | Bucur, Dorin Cito, Simone |
| description | This paper is motivated by the study of the existence of optimal domains maximizing the
k
th Robin Laplacian eigenvalue among sets of prescribed measure, in the case of a negative boundary parameter. We answer positively to this question and prove an existence result in the class of measurable sets and for quite general spectral functionals. The key tools of our analysis rely on tight isodiametric and isoperimetric geometric controls of the eigenvalues. In two dimensions of the space, under simply connectedness assumptions, further qualitative properties are obtained on the optimal sets. |
| doi_str_mv | 10.1007/s12220-019-00245-9 |
| format | Article |
| fullrecord | <record><control><sourceid>gale_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_04723995v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A707340068</galeid><sourcerecordid>A707340068</sourcerecordid><originalsourceid>FETCH-LOGICAL-c392t-78858de3750559f9c438488da36b3051a26359ddaafac51f83c8536ab2be80803</originalsourceid><addsrcrecordid>eNp9kU9r3DAQxU1poWnaL9CToKcenI4ky5Z62y75U1iSEFLopYhZebxR8EpbybvQb19tHNJbmYNmht8bnnhV9ZHDGQfovmQuhIAauKkBRKNq86o64Uo9jT9flx4U1K0R7dvqXc6PAE0rm-6k-nVJcUtT8o4tY5hSHFkc2PRA7C6ufWAr3I3oPAZ27jcUDjjuKX9l9wVYYqYjfE0bnPyB2Le4Dz2mP-wWE5ajlN5XbwYcM314fk-rHxfn98urenVz-X25WNVOGjHVndZK9yQ7BcXyYFwjdaN1j7JdS1AcRSuV6XvEAZ3ig5ZOK9niWqxJgwZ5Wn2e7z7gaHfJb4sLG9Hbq8XKHnfQdEIaow68sJ9mdpfi7_KZyT7GfQrFnhVNJzUIyUWhzmZqgyNZH4Y4JXSletp6FwMNvuwXHXSyAWh1EYhZ4FLMOdHw4oODPWZk54xsycg-ZWRNEclZlAscNpT-efmP6i861ZG_</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2473802312</pqid></control><display><type>article</type><title>Geometric Control of the Robin Laplacian Eigenvalues: The Case of Negative Boundary Parameter</title><source>Springer Nature - Complete Springer Journals</source><creator>Bucur, Dorin ; Cito, Simone</creator><creatorcontrib>Bucur, Dorin ; Cito, Simone</creatorcontrib><description>This paper is motivated by the study of the existence of optimal domains maximizing the
k
th Robin Laplacian eigenvalue among sets of prescribed measure, in the case of a negative boundary parameter. We answer positively to this question and prove an existence result in the class of measurable sets and for quite general spectral functionals. The key tools of our analysis rely on tight isodiametric and isoperimetric geometric controls of the eigenvalues. In two dimensions of the space, under simply connectedness assumptions, further qualitative properties are obtained on the optimal sets.</description><identifier>ISSN: 1050-6926</identifier><identifier>EISSN: 1559-002X</identifier><identifier>DOI: 10.1007/s12220-019-00245-9</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Analysis of PDEs ; Convex and Discrete Geometry ; Differential Geometry ; Dynamical Systems and Ergodic Theory ; Eigenvalues ; Fourier Analysis ; Geometry ; Global Analysis and Analysis on Manifolds ; Mathematics ; Mathematics and Statistics ; Optimization ; Parameters ; Set theory</subject><ispartof>The Journal of Geometric Analysis, 2020-12, Vol.30 (4), p.4356-4385</ispartof><rights>Mathematica Josephina, Inc. 2019</rights><rights>COPYRIGHT 2020 Springer</rights><rights>Mathematica Josephina, Inc. 2019.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c392t-78858de3750559f9c438488da36b3051a26359ddaafac51f83c8536ab2be80803</citedby><cites>FETCH-LOGICAL-c392t-78858de3750559f9c438488da36b3051a26359ddaafac51f83c8536ab2be80803</cites><orcidid>0000-0002-8331-8481</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12220-019-00245-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12220-019-00245-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,776,780,881,27901,27902,41464,42533,51294</link.rule.ids><backlink>$$Uhttps://hal.science/hal-04723995$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Bucur, Dorin</creatorcontrib><creatorcontrib>Cito, Simone</creatorcontrib><title>Geometric Control of the Robin Laplacian Eigenvalues: The Case of Negative Boundary Parameter</title><title>The Journal of Geometric Analysis</title><addtitle>J Geom Anal</addtitle><description>This paper is motivated by the study of the existence of optimal domains maximizing the
k
th Robin Laplacian eigenvalue among sets of prescribed measure, in the case of a negative boundary parameter. We answer positively to this question and prove an existence result in the class of measurable sets and for quite general spectral functionals. The key tools of our analysis rely on tight isodiametric and isoperimetric geometric controls of the eigenvalues. In two dimensions of the space, under simply connectedness assumptions, further qualitative properties are obtained on the optimal sets.</description><subject>Abstract Harmonic Analysis</subject><subject>Analysis of PDEs</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Eigenvalues</subject><subject>Fourier Analysis</subject><subject>Geometry</subject><subject>Global Analysis and Analysis on Manifolds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Optimization</subject><subject>Parameters</subject><subject>Set theory</subject><issn>1050-6926</issn><issn>1559-002X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kU9r3DAQxU1poWnaL9CToKcenI4ky5Z62y75U1iSEFLopYhZebxR8EpbybvQb19tHNJbmYNmht8bnnhV9ZHDGQfovmQuhIAauKkBRKNq86o64Uo9jT9flx4U1K0R7dvqXc6PAE0rm-6k-nVJcUtT8o4tY5hSHFkc2PRA7C6ufWAr3I3oPAZ27jcUDjjuKX9l9wVYYqYjfE0bnPyB2Le4Dz2mP-wWE5ajlN5XbwYcM314fk-rHxfn98urenVz-X25WNVOGjHVndZK9yQ7BcXyYFwjdaN1j7JdS1AcRSuV6XvEAZ3ig5ZOK9niWqxJgwZ5Wn2e7z7gaHfJb4sLG9Hbq8XKHnfQdEIaow68sJ9mdpfi7_KZyT7GfQrFnhVNJzUIyUWhzmZqgyNZH4Y4JXSletp6FwMNvuwXHXSyAWh1EYhZ4FLMOdHw4oODPWZk54xsycg-ZWRNEclZlAscNpT-efmP6i861ZG_</recordid><startdate>20201201</startdate><enddate>20201201</enddate><creator>Bucur, Dorin</creator><creator>Cito, Simone</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>IAO</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-8331-8481</orcidid></search><sort><creationdate>20201201</creationdate><title>Geometric Control of the Robin Laplacian Eigenvalues: The Case of Negative Boundary Parameter</title><author>Bucur, Dorin ; Cito, Simone</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c392t-78858de3750559f9c438488da36b3051a26359ddaafac51f83c8536ab2be80803</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Analysis of PDEs</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Eigenvalues</topic><topic>Fourier Analysis</topic><topic>Geometry</topic><topic>Global Analysis and Analysis on Manifolds</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Optimization</topic><topic>Parameters</topic><topic>Set theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bucur, Dorin</creatorcontrib><creatorcontrib>Cito, Simone</creatorcontrib><collection>CrossRef</collection><collection>Gale Academic OneFile</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>The Journal of Geometric Analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bucur, Dorin</au><au>Cito, Simone</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Geometric Control of the Robin Laplacian Eigenvalues: The Case of Negative Boundary Parameter</atitle><jtitle>The Journal of Geometric Analysis</jtitle><stitle>J Geom Anal</stitle><date>2020-12-01</date><risdate>2020</risdate><volume>30</volume><issue>4</issue><spage>4356</spage><epage>4385</epage><pages>4356-4385</pages><issn>1050-6926</issn><eissn>1559-002X</eissn><abstract>This paper is motivated by the study of the existence of optimal domains maximizing the
k
th Robin Laplacian eigenvalue among sets of prescribed measure, in the case of a negative boundary parameter. We answer positively to this question and prove an existence result in the class of measurable sets and for quite general spectral functionals. The key tools of our analysis rely on tight isodiametric and isoperimetric geometric controls of the eigenvalues. In two dimensions of the space, under simply connectedness assumptions, further qualitative properties are obtained on the optimal sets.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s12220-019-00245-9</doi><tpages>30</tpages><orcidid>https://orcid.org/0000-0002-8331-8481</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1050-6926 |
| ispartof | The Journal of Geometric Analysis, 2020-12, Vol.30 (4), p.4356-4385 |
| issn | 1050-6926 1559-002X |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_04723995v1 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Abstract Harmonic Analysis Analysis of PDEs Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Eigenvalues Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics Optimization Parameters Set theory |
| title | Geometric Control of the Robin Laplacian Eigenvalues: The Case of Negative Boundary Parameter |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-30T16%3A59%3A25IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Geometric%20Control%20of%20the%20Robin%20Laplacian%20Eigenvalues:%20The%20Case%20of%20Negative%20Boundary%20Parameter&rft.jtitle=The%20Journal%20of%20Geometric%20Analysis&rft.au=Bucur,%20Dorin&rft.date=2020-12-01&rft.volume=30&rft.issue=4&rft.spage=4356&rft.epage=4385&rft.pages=4356-4385&rft.issn=1050-6926&rft.eissn=1559-002X&rft_id=info:doi/10.1007/s12220-019-00245-9&rft_dat=%3Cgale_hal_p%3EA707340068%3C/gale_hal_p%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2473802312&rft_id=info:pmid/&rft_galeid=A707340068&rfr_iscdi=true |