Direct Methods for Pseudo-relativistic Schrödinger Operators
In this paper, we establish various maximal principles and develop the direct moving planes and sliding methods for equations involving the physically interesting (nonlocal) pseudo-relativistic Schrödinger operators ( - Δ + m 2 ) s with s ∈ ( 0 , 1 ) and mass m > 0 . As a consequence, we also der...
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| Veröffentlicht in: | The Journal of Geometric Analysis 2021-06, Vol.31 (6), p.5555-5618 |
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| container_title | The Journal of Geometric Analysis |
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| creator | Dai, Wei Qin, Guolin Wu, Dan |
| description | In this paper, we establish various maximal principles and develop the direct moving planes and sliding methods for equations involving the physically interesting (nonlocal) pseudo-relativistic Schrödinger operators
(
-
Δ
+
m
2
)
s
with
s
∈
(
0
,
1
)
and mass
m
>
0
. As a consequence, we also derive multiple applications of these direct methods. For instance, we prove monotonicity, symmetry and uniqueness results for solutions to various equations involving the operators
(
-
Δ
+
m
2
)
s
in bounded or unbounded domains with certain geometrical structures (e.g., coercive epigraph and epigraph), including pseudo-relativistic Schrödinger equations, 3D boson star equations and the equations with De Giorgi-type nonlinearities. When
m
=
0
and
s
=
1
, equations with De Giorgi-type nonlinearities are related to De Giorgi conjecture connected with minimal surfaces and the scalar Ginzburg–Landau functional associated to harmonic map. |
| doi_str_mv | 10.1007/s12220-020-00492-1 |
| format | Article |
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(
-
Δ
+
m
2
)
s
with
s
∈
(
0
,
1
)
and mass
m
>
0
. As a consequence, we also derive multiple applications of these direct methods. For instance, we prove monotonicity, symmetry and uniqueness results for solutions to various equations involving the operators
(
-
Δ
+
m
2
)
s
in bounded or unbounded domains with certain geometrical structures (e.g., coercive epigraph and epigraph), including pseudo-relativistic Schrödinger equations, 3D boson star equations and the equations with De Giorgi-type nonlinearities. When
m
=
0
and
s
=
1
, equations with De Giorgi-type nonlinearities are related to De Giorgi conjecture connected with minimal surfaces and the scalar Ginzburg–Landau functional associated to harmonic map.</description><identifier>ISSN: 1050-6926</identifier><identifier>EISSN: 1559-002X</identifier><identifier>DOI: 10.1007/s12220-020-00492-1</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Convex and Discrete Geometry ; Differential Geometry ; Dynamical Systems and Ergodic Theory ; Fourier Analysis ; Geometry ; Global Analysis and Analysis on Manifolds ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Minimal surfaces ; Nonlinearity ; Operators (mathematics) ; Relativistic effects ; Schrodinger equation</subject><ispartof>The Journal of Geometric Analysis, 2021-06, Vol.31 (6), p.5555-5618</ispartof><rights>Mathematica Josephina, Inc. 2020</rights><rights>COPYRIGHT 2021 Springer</rights><rights>Mathematica Josephina, Inc. 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c358t-988d37558bad7cc70d8331e0a834c46f6c14bcff3306369b5504f4fb49f572923</citedby><cites>FETCH-LOGICAL-c358t-988d37558bad7cc70d8331e0a834c46f6c14bcff3306369b5504f4fb49f572923</cites><orcidid>0000-0002-2395-8751</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/s12220-020-00492-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12220-020-00492-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Dai, Wei</creatorcontrib><creatorcontrib>Qin, Guolin</creatorcontrib><creatorcontrib>Wu, Dan</creatorcontrib><title>Direct Methods for Pseudo-relativistic Schrödinger Operators</title><title>The Journal of Geometric Analysis</title><addtitle>J Geom Anal</addtitle><description>In this paper, we establish various maximal principles and develop the direct moving planes and sliding methods for equations involving the physically interesting (nonlocal) pseudo-relativistic Schrödinger operators
(
-
Δ
+
m
2
)
s
with
s
∈
(
0
,
1
)
and mass
m
>
0
. As a consequence, we also derive multiple applications of these direct methods. For instance, we prove monotonicity, symmetry and uniqueness results for solutions to various equations involving the operators
(
-
Δ
+
m
2
)
s
in bounded or unbounded domains with certain geometrical structures (e.g., coercive epigraph and epigraph), including pseudo-relativistic Schrödinger equations, 3D boson star equations and the equations with De Giorgi-type nonlinearities. When
m
=
0
and
s
=
1
, equations with De Giorgi-type nonlinearities are related to De Giorgi conjecture connected with minimal surfaces and the scalar Ginzburg–Landau functional associated to harmonic map.</description><subject>Abstract Harmonic Analysis</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Fourier Analysis</subject><subject>Geometry</subject><subject>Global Analysis and Analysis on Manifolds</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Minimal surfaces</subject><subject>Nonlinearity</subject><subject>Operators (mathematics)</subject><subject>Relativistic effects</subject><subject>Schrodinger equation</subject><issn>1050-6926</issn><issn>1559-002X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKAzEUhoMoWKsv4GrA9dTcM7NwUeoVKhVUcBcymaRNaSc1SQVfzBfwxcwwgjsJh1z4v5zDB8A5ghMEobiMCGMMS9gXpDUu0QEYIcbqfMVvh_kMGSx5jfkxOIlxnUOcUDECV9cuGJ2KR5NWvo2F9aF4imbf-jKYjUruw8XkdPGsV-H7q3Xd0oRisTNBJR_iKTiyahPN2e8-Bq-3Ny-z-3K-uHuYTeelJqxKZV1VLRGMVY1qhdYCthUhyEBVEaopt1wj2mhrCYGc8LphDFJLbUNrywSuMRmDi-HfXfDvexOTXPt96HJLiRnhjOCM5dRkSC3VxkjXWZ-C0nm1Zuu074x1-X0qoCAUZl0ZwAOgg48xGCt3wW1V-JQIyt6rHLxK2FfvVaIMkQGKOdzr-JvlH-oHnod6FQ</recordid><startdate>20210601</startdate><enddate>20210601</enddate><creator>Dai, Wei</creator><creator>Qin, Guolin</creator><creator>Wu, Dan</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>IAO</scope><orcidid>https://orcid.org/0000-0002-2395-8751</orcidid></search><sort><creationdate>20210601</creationdate><title>Direct Methods for Pseudo-relativistic Schrödinger Operators</title><author>Dai, Wei ; Qin, Guolin ; Wu, Dan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c358t-988d37558bad7cc70d8331e0a834c46f6c14bcff3306369b5504f4fb49f572923</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Fourier Analysis</topic><topic>Geometry</topic><topic>Global Analysis and Analysis on Manifolds</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Minimal surfaces</topic><topic>Nonlinearity</topic><topic>Operators (mathematics)</topic><topic>Relativistic effects</topic><topic>Schrodinger equation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dai, Wei</creatorcontrib><creatorcontrib>Qin, Guolin</creatorcontrib><creatorcontrib>Wu, Dan</creatorcontrib><collection>CrossRef</collection><collection>Gale Academic OneFile</collection><jtitle>The Journal of Geometric Analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dai, Wei</au><au>Qin, Guolin</au><au>Wu, Dan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Direct Methods for Pseudo-relativistic Schrödinger Operators</atitle><jtitle>The Journal of Geometric Analysis</jtitle><stitle>J Geom Anal</stitle><date>2021-06-01</date><risdate>2021</risdate><volume>31</volume><issue>6</issue><spage>5555</spage><epage>5618</epage><pages>5555-5618</pages><issn>1050-6926</issn><eissn>1559-002X</eissn><abstract>In this paper, we establish various maximal principles and develop the direct moving planes and sliding methods for equations involving the physically interesting (nonlocal) pseudo-relativistic Schrödinger operators
(
-
Δ
+
m
2
)
s
with
s
∈
(
0
,
1
)
and mass
m
>
0
. As a consequence, we also derive multiple applications of these direct methods. For instance, we prove monotonicity, symmetry and uniqueness results for solutions to various equations involving the operators
(
-
Δ
+
m
2
)
s
in bounded or unbounded domains with certain geometrical structures (e.g., coercive epigraph and epigraph), including pseudo-relativistic Schrödinger equations, 3D boson star equations and the equations with De Giorgi-type nonlinearities. When
m
=
0
and
s
=
1
, equations with De Giorgi-type nonlinearities are related to De Giorgi conjecture connected with minimal surfaces and the scalar Ginzburg–Landau functional associated to harmonic map.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s12220-020-00492-1</doi><tpages>64</tpages><orcidid>https://orcid.org/0000-0002-2395-8751</orcidid></addata></record> |
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| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematical analysis Mathematics Mathematics and Statistics Minimal surfaces Nonlinearity Operators (mathematics) Relativistic effects Schrodinger equation |
| title | Direct Methods for Pseudo-relativistic Schrödinger Operators |
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