Existence of energy-minimal diffeomorphisms between doubly connected domains
The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Among all homeomorphisms between bounded doubly connected domains such that Mod Ω≤Mod Ω ∗ there exists, unique up to conformal authomorphisms of Ω , an energy-minimal diffeomorphism ....
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| Veröffentlicht in: | Inventiones mathematicae 2011-12, Vol.186 (3), p.667-707 |
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| container_title | Inventiones mathematicae |
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| creator | Iwaniec, Tadeusz Koh, Ngin-Tee Kovalev, Leonid V. Onninen, Jani |
| description | The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy.
Among all homeomorphisms
between bounded doubly connected domains such that
Mod Ω≤Mod Ω
∗
there exists, unique up to conformal authomorphisms of
Ω
, an energy-minimal diffeomorphism
.
Here Mod stands for the conformal modulus of a domain. No boundary conditions are imposed on
f
. Although any energy-minimal diffeomorphism is harmonic, our results underline the major difference between the existence of harmonic diffeomorphisms and the existence of the energy-minimal diffeomorphisms. The existence of globally invertible energy-minimal mappings is of primary pursuit in the mathematical models of nonlinear elasticity and is also of interest in computer graphics. |
| doi_str_mv | 10.1007/s00222-011-0327-6 |
| format | Article |
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Among all homeomorphisms
between bounded doubly connected domains such that
Mod Ω≤Mod Ω
∗
there exists, unique up to conformal authomorphisms of
Ω
, an energy-minimal diffeomorphism
.
Here Mod stands for the conformal modulus of a domain. No boundary conditions are imposed on
f
. Although any energy-minimal diffeomorphism is harmonic, our results underline the major difference between the existence of harmonic diffeomorphisms and the existence of the energy-minimal diffeomorphisms. The existence of globally invertible energy-minimal mappings is of primary pursuit in the mathematical models of nonlinear elasticity and is also of interest in computer graphics.</description><identifier>ISSN: 0020-9910</identifier><identifier>EISSN: 1432-1297</identifier><identifier>DOI: 10.1007/s00222-011-0327-6</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer-Verlag</publisher><subject>Mathematics ; Mathematics and Statistics</subject><ispartof>Inventiones mathematicae, 2011-12, Vol.186 (3), p.667-707</ispartof><rights>Springer-Verlag 2011</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c315t-29eafd313cc222f13b497643d607e0c1e5821e8c88afd96f171a1fe72c06e4233</citedby><cites>FETCH-LOGICAL-c315t-29eafd313cc222f13b497643d607e0c1e5821e8c88afd96f171a1fe72c06e4233</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00222-011-0327-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00222-011-0327-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Iwaniec, Tadeusz</creatorcontrib><creatorcontrib>Koh, Ngin-Tee</creatorcontrib><creatorcontrib>Kovalev, Leonid V.</creatorcontrib><creatorcontrib>Onninen, Jani</creatorcontrib><title>Existence of energy-minimal diffeomorphisms between doubly connected domains</title><title>Inventiones mathematicae</title><addtitle>Invent. math</addtitle><description>The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy.
Among all homeomorphisms
between bounded doubly connected domains such that
Mod Ω≤Mod Ω
∗
there exists, unique up to conformal authomorphisms of
Ω
, an energy-minimal diffeomorphism
.
Here Mod stands for the conformal modulus of a domain. No boundary conditions are imposed on
f
. Although any energy-minimal diffeomorphism is harmonic, our results underline the major difference between the existence of harmonic diffeomorphisms and the existence of the energy-minimal diffeomorphisms. 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Koh, Ngin-Tee ; Kovalev, Leonid V. ; Onninen, Jani</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c315t-29eafd313cc222f13b497643d607e0c1e5821e8c88afd96f171a1fe72c06e4233</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Iwaniec, Tadeusz</creatorcontrib><creatorcontrib>Koh, Ngin-Tee</creatorcontrib><creatorcontrib>Kovalev, Leonid V.</creatorcontrib><creatorcontrib>Onninen, Jani</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Inventiones mathematicae</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Iwaniec, Tadeusz</au><au>Koh, Ngin-Tee</au><au>Kovalev, Leonid V.</au><au>Onninen, Jani</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence of energy-minimal diffeomorphisms between doubly connected domains</atitle><jtitle>Inventiones mathematicae</jtitle><stitle>Invent. math</stitle><date>2011-12-01</date><risdate>2011</risdate><volume>186</volume><issue>3</issue><spage>667</spage><epage>707</epage><pages>667-707</pages><issn>0020-9910</issn><eissn>1432-1297</eissn><abstract>The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy.
Among all homeomorphisms
between bounded doubly connected domains such that
Mod Ω≤Mod Ω
∗
there exists, unique up to conformal authomorphisms of
Ω
, an energy-minimal diffeomorphism
.
Here Mod stands for the conformal modulus of a domain. No boundary conditions are imposed on
f
. Although any energy-minimal diffeomorphism is harmonic, our results underline the major difference between the existence of harmonic diffeomorphisms and the existence of the energy-minimal diffeomorphisms. The existence of globally invertible energy-minimal mappings is of primary pursuit in the mathematical models of nonlinear elasticity and is also of interest in computer graphics.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer-Verlag</pub><doi>10.1007/s00222-011-0327-6</doi><tpages>41</tpages></addata></record> |
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| language | eng |
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| subjects | Mathematics Mathematics and Statistics |
| title | Existence of energy-minimal diffeomorphisms between doubly connected domains |
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