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On Singular Points of Solutions of the Minimal Surface Equation on Sets of Positive Measure
It is shown that, for any compact set K ⊂ ℝ n ( n ⩾ 2) of positive Lebesgue measure and any bounded domain G ⊃ K , there exists a function in the Hölder class C 1,1 ( G ) that is a solution of the minimal surface equation in G \ K and cannot be extended from G \ K to G as a solution of this equation...
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| Published in: | Functional analysis and its applications 2018, Vol.52 (1), p.62-65 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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| Online Access: | Get full text |
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| cites | cdi_FETCH-LOGICAL-c268t-4c57b95cf1514ddf27f54e8a6fe495aed36d4c231ea0aec55e700a01864dbdff3 |
| container_end_page | 65 |
| container_issue | 1 |
| container_start_page | 62 |
| container_title | Functional analysis and its applications |
| container_volume | 52 |
| creator | Pokrovskii, A. V. |
| description | It is shown that, for any compact set
K
⊂ ℝ
n
(
n
⩾ 2) of positive Lebesgue measure and any bounded domain
G
⊃
K
, there exists a function in the Hölder class
C
1,1
(
G
) that is a solution of the minimal surface equation in
G
\
K
and cannot be extended from
G
\
K
to
G
as a solution of this equation. |
| doi_str_mv | 10.1007/s10688-018-0209-4 |
| format | article |
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K
⊂ ℝ
n
(
n
⩾ 2) of positive Lebesgue measure and any bounded domain
G
⊃
K
, there exists a function in the Hölder class
C
1,1
(
G
) that is a solution of the minimal surface equation in
G
\
K
and cannot be extended from
G
\
K
to
G
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K
⊂ ℝ
n
(
n
⩾ 2) of positive Lebesgue measure and any bounded domain
G
⊃
K
, there exists a function in the Hölder class
C
1,1
(
G
) that is a solution of the minimal surface equation in
G
\
K
and cannot be extended from
G
\
K
to
G
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K
⊂ ℝ
n
(
n
⩾ 2) of positive Lebesgue measure and any bounded domain
G
⊃
K
, there exists a function in the Hölder class
C
1,1
(
G
) that is a solution of the minimal surface equation in
G
\
K
and cannot be extended from
G
\
K
to
G
as a solution of this equation.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10688-018-0209-4</doi><tpages>4</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0016-2663 |
| ispartof | Functional analysis and its applications, 2018, Vol.52 (1), p.62-65 |
| issn | 0016-2663 1573-8485 |
| language | eng |
| recordid | cdi_proquest_journals_2019526494 |
| source | Springer Nature |
| subjects | Analysis Brief Communications Functional Analysis Mathematics Mathematics and Statistics |
| title | On Singular Points of Solutions of the Minimal Surface Equation on Sets of Positive Measure |
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