Density of polyhedral partitions
We prove the density of polyhedral partitions in the set of finite Caccioppoli partitions. Precisely, given a decomposition u of a bounded Lipschitz set Ω ⊂ R n into finitely many subsets of finite perimeter and ε > 0 , we prove that u is ε -close to a small deformation of a polyhedral decomposit...
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| Veröffentlicht in: | Calculus of variations and partial differential equations 2017-04, Vol.56 (2), p.1-10, Article 28 |
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| container_title | Calculus of variations and partial differential equations |
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| creator | Braides, Andrea Conti, Sergio Garroni, Adriana |
| description | We prove the density of polyhedral partitions in the set of finite Caccioppoli partitions. Precisely, given a decomposition
u
of a bounded Lipschitz set
Ω
⊂
R
n
into finitely many subsets of finite perimeter and
ε
>
0
, we prove that
u
is
ε
-close to a small deformation of a polyhedral decomposition
v
ε
, in the sense that there is a
C
1
diffeomorphism
f
ε
:
R
n
→
R
n
which is
ε
-close to the identity and such that
u
∘
f
ε
-
v
ε
is
ε
-small in the strong
BV
norm. This implies that the energy of
u
is close to that of
v
ε
for a large class of energies defined on partitions. |
| doi_str_mv | 10.1007/s00526-017-1108-x |
| format | Article |
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u
of a bounded Lipschitz set
Ω
⊂
R
n
into finitely many subsets of finite perimeter and
ε
>
0
, we prove that
u
is
ε
-close to a small deformation of a polyhedral decomposition
v
ε
, in the sense that there is a
C
1
diffeomorphism
f
ε
:
R
n
→
R
n
which is
ε
-close to the identity and such that
u
∘
f
ε
-
v
ε
is
ε
-small in the strong
BV
norm. This implies that the energy of
u
is close to that of
v
ε
for a large class of energies defined on partitions.</description><identifier>ISSN: 0944-2669</identifier><identifier>EISSN: 1432-0835</identifier><identifier>DOI: 10.1007/s00526-017-1108-x</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Calculus of Variations and Optimal Control; Optimization ; Control ; Decomposition ; Deformation ; Density ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Partitions (mathematics) ; Systems Theory ; Theoretical</subject><ispartof>Calculus of variations and partial differential equations, 2017-04, Vol.56 (2), p.1-10, Article 28</ispartof><rights>Springer-Verlag Berlin Heidelberg 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-a56dd41f578265630206d81a114d9e54682d680455790b5c0fb3ad8dd85c041e3</citedby><cites>FETCH-LOGICAL-c316t-a56dd41f578265630206d81a114d9e54682d680455790b5c0fb3ad8dd85c041e3</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/s00526-017-1108-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00526-017-1108-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Braides, Andrea</creatorcontrib><creatorcontrib>Conti, Sergio</creatorcontrib><creatorcontrib>Garroni, Adriana</creatorcontrib><title>Density of polyhedral partitions</title><title>Calculus of variations and partial differential equations</title><addtitle>Calc. Var</addtitle><description>We prove the density of polyhedral partitions in the set of finite Caccioppoli partitions. Precisely, given a decomposition
u
of a bounded Lipschitz set
Ω
⊂
R
n
into finitely many subsets of finite perimeter and
ε
>
0
, we prove that
u
is
ε
-close to a small deformation of a polyhedral decomposition
v
ε
, in the sense that there is a
C
1
diffeomorphism
f
ε
:
R
n
→
R
n
which is
ε
-close to the identity and such that
u
∘
f
ε
-
v
ε
is
ε
-small in the strong
BV
norm. This implies that the energy of
u
is close to that of
v
ε
for a large class of energies defined on partitions.</description><subject>Analysis</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Decomposition</subject><subject>Deformation</subject><subject>Density</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partitions (mathematics)</subject><subject>Systems Theory</subject><subject>Theoretical</subject><issn>0944-2669</issn><issn>1432-0835</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LxDAURYMoOI7-AHcF19H38tV0KaOOwoAbXYdMk2qH2tSkA9N_b4YKrly9u7jnPjiEXCPcIkB5lwAkUxSwpIig6eGELFBwRkFzeUoWUAlBmVLVOblIaQeAUjOxIMWD71M7TkVoiiF006d30XbFYOPYjm3o0yU5a2yX_NXvXZL3p8e31TPdvK5fVvcbWnNUI7VSOSewkaVmSioODJTTaBGFq7wUSjOnNAgpywq2soZmy63TzumcBXq-JDfz7hDD996n0ezCPvb5pclTXEnOeJVbOLfqGFKKvjFDbL9snAyCOYowswiTRZijCHPIDJuZlLv9h49_y_9DP1V3Xn0</recordid><startdate>20170401</startdate><enddate>20170401</enddate><creator>Braides, Andrea</creator><creator>Conti, Sergio</creator><creator>Garroni, Adriana</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20170401</creationdate><title>Density of polyhedral partitions</title><author>Braides, Andrea ; Conti, Sergio ; Garroni, Adriana</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-a56dd41f578265630206d81a114d9e54682d680455790b5c0fb3ad8dd85c041e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Analysis</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Decomposition</topic><topic>Deformation</topic><topic>Density</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partitions (mathematics)</topic><topic>Systems Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Braides, Andrea</creatorcontrib><creatorcontrib>Conti, Sergio</creatorcontrib><creatorcontrib>Garroni, Adriana</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Calculus of variations and partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Braides, Andrea</au><au>Conti, Sergio</au><au>Garroni, Adriana</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Density of polyhedral partitions</atitle><jtitle>Calculus of variations and partial differential equations</jtitle><stitle>Calc. Var</stitle><date>2017-04-01</date><risdate>2017</risdate><volume>56</volume><issue>2</issue><spage>1</spage><epage>10</epage><pages>1-10</pages><artnum>28</artnum><issn>0944-2669</issn><eissn>1432-0835</eissn><abstract>We prove the density of polyhedral partitions in the set of finite Caccioppoli partitions. Precisely, given a decomposition
u
of a bounded Lipschitz set
Ω
⊂
R
n
into finitely many subsets of finite perimeter and
ε
>
0
, we prove that
u
is
ε
-close to a small deformation of a polyhedral decomposition
v
ε
, in the sense that there is a
C
1
diffeomorphism
f
ε
:
R
n
→
R
n
which is
ε
-close to the identity and such that
u
∘
f
ε
-
v
ε
is
ε
-small in the strong
BV
norm. This implies that the energy of
u
is close to that of
v
ε
for a large class of energies defined on partitions.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00526-017-1108-x</doi><tpages>10</tpages></addata></record> |
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| language | eng |
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| source | SpringerLink Journals |
| subjects | Analysis Calculus of Variations and Optimal Control Optimization Control Decomposition Deformation Density Mathematical and Computational Physics Mathematics Mathematics and Statistics Partitions (mathematics) Systems Theory Theoretical |
| title | Density of polyhedral partitions |
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