Weak Solutions to the Complex Hessian Type Equations for Arbitrary Measures
Abstract We study the complex equations of Hessian type (ddcu)m∧βn-m=F(u,.)dμ,$$\begin{aligned} (dd^c u)^m\wedge \beta ^{n-m}=F(u,.)d\mu , \end{aligned}$$where $$\mu $$ is a positive Borel measure defined on an m-hyperconvex domain of $${\mathbb {C}}^{n}$$, m is an integer such that $$1\le m\le n$$...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Amal, Hichame [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Nature Switzerland AG 2020 |
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| Übergeordnetes Werk: |
Enthalten in: Complex analysis and operator theory - Springer International Publishing, 2007, 14(2020), 8 vom: 13. Okt. |
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| Übergeordnetes Werk: |
volume:14 ; year:2020 ; number:8 ; day:13 ; month:10 |
| Links: |
|---|
| DOI / URN: |
10.1007/s11785-020-01044-9 |
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OLC2121385142 |
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| 520 | |a Abstract We study the complex equations of Hessian type (ddcu)m∧βn-m=F(u,.)dμ,$$\begin{aligned} (dd^c u)^m\wedge \beta ^{n-m}=F(u,.)d\mu , \end{aligned}$$where $$\mu $$ is a positive Borel measure defined on an m-hyperconvex domain of $${\mathbb {C}}^{n}$$, m is an integer such that $$1\le m\le n$$ and $$\beta :=dd^{c}\vert z\vert ^{2}$$ is the standard kähler form in $${\mathbb {C}}^{n}. $$ We show that, under some regularity conditions on the density F, if this equation admits a (weak) subsolution in $$\Omega $$, then it admits a (weak) solution with a prescribed least maximal m-subharmonic majorant in $$\Omega $$. | ||
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10.1007/s11785-020-01044-9 doi (DE-627)OLC2121385142 (DE-He213)s11785-020-01044-9-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Amal, Hichame verfasserin aut Weak Solutions to the Complex Hessian Type Equations for Arbitrary Measures 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature Switzerland AG 2020 Abstract We study the complex equations of Hessian type (ddcu)m∧βn-m=F(u,.)dμ,$$\begin{aligned} (dd^c u)^m\wedge \beta ^{n-m}=F(u,.)d\mu , \end{aligned}$$where $$\mu $$ is a positive Borel measure defined on an m-hyperconvex domain of $${\mathbb {C}}^{n}$$, m is an integer such that $$1\le m\le n$$ and $$\beta :=dd^{c}\vert z\vert ^{2}$$ is the standard kähler form in $${\mathbb {C}}^{n}. $$ We show that, under some regularity conditions on the density F, if this equation admits a (weak) subsolution in $$\Omega $$, then it admits a (weak) solution with a prescribed least maximal m-subharmonic majorant in $$\Omega $$. Complex Hessian equations -subharmonic functions Dirichlet problem -hyperconvex domain Maximal -subharmonic function Asserda, Saïd aut El Gasmi, Ayoub (orcid)0000-0003-0453-2074 aut Enthalten in Complex analysis and operator theory Springer International Publishing, 2007 14(2020), 8 vom: 13. Okt. (DE-627)565301047 (DE-600)2425163-X (DE-576)409490164 1661-8254 nnns volume:14 year:2020 number:8 day:13 month:10 https://doi.org/10.1007/s11785-020-01044-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 14 2020 8 13 10 |
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10.1007/s11785-020-01044-9 doi (DE-627)OLC2121385142 (DE-He213)s11785-020-01044-9-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Amal, Hichame verfasserin aut Weak Solutions to the Complex Hessian Type Equations for Arbitrary Measures 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature Switzerland AG 2020 Abstract We study the complex equations of Hessian type (ddcu)m∧βn-m=F(u,.)dμ,$$\begin{aligned} (dd^c u)^m\wedge \beta ^{n-m}=F(u,.)d\mu , \end{aligned}$$where $$\mu $$ is a positive Borel measure defined on an m-hyperconvex domain of $${\mathbb {C}}^{n}$$, m is an integer such that $$1\le m\le n$$ and $$\beta :=dd^{c}\vert z\vert ^{2}$$ is the standard kähler form in $${\mathbb {C}}^{n}. $$ We show that, under some regularity conditions on the density F, if this equation admits a (weak) subsolution in $$\Omega $$, then it admits a (weak) solution with a prescribed least maximal m-subharmonic majorant in $$\Omega $$. Complex Hessian equations -subharmonic functions Dirichlet problem -hyperconvex domain Maximal -subharmonic function Asserda, Saïd aut El Gasmi, Ayoub (orcid)0000-0003-0453-2074 aut Enthalten in Complex analysis and operator theory Springer International Publishing, 2007 14(2020), 8 vom: 13. Okt. (DE-627)565301047 (DE-600)2425163-X (DE-576)409490164 1661-8254 nnns volume:14 year:2020 number:8 day:13 month:10 https://doi.org/10.1007/s11785-020-01044-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 14 2020 8 13 10 |
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10.1007/s11785-020-01044-9 doi (DE-627)OLC2121385142 (DE-He213)s11785-020-01044-9-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Amal, Hichame verfasserin aut Weak Solutions to the Complex Hessian Type Equations for Arbitrary Measures 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature Switzerland AG 2020 Abstract We study the complex equations of Hessian type (ddcu)m∧βn-m=F(u,.)dμ,$$\begin{aligned} (dd^c u)^m\wedge \beta ^{n-m}=F(u,.)d\mu , \end{aligned}$$where $$\mu $$ is a positive Borel measure defined on an m-hyperconvex domain of $${\mathbb {C}}^{n}$$, m is an integer such that $$1\le m\le n$$ and $$\beta :=dd^{c}\vert z\vert ^{2}$$ is the standard kähler form in $${\mathbb {C}}^{n}. $$ We show that, under some regularity conditions on the density F, if this equation admits a (weak) subsolution in $$\Omega $$, then it admits a (weak) solution with a prescribed least maximal m-subharmonic majorant in $$\Omega $$. Complex Hessian equations -subharmonic functions Dirichlet problem -hyperconvex domain Maximal -subharmonic function Asserda, Saïd aut El Gasmi, Ayoub (orcid)0000-0003-0453-2074 aut Enthalten in Complex analysis and operator theory Springer International Publishing, 2007 14(2020), 8 vom: 13. Okt. (DE-627)565301047 (DE-600)2425163-X (DE-576)409490164 1661-8254 nnns volume:14 year:2020 number:8 day:13 month:10 https://doi.org/10.1007/s11785-020-01044-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 14 2020 8 13 10 |
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10.1007/s11785-020-01044-9 doi (DE-627)OLC2121385142 (DE-He213)s11785-020-01044-9-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Amal, Hichame verfasserin aut Weak Solutions to the Complex Hessian Type Equations for Arbitrary Measures 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature Switzerland AG 2020 Abstract We study the complex equations of Hessian type (ddcu)m∧βn-m=F(u,.)dμ,$$\begin{aligned} (dd^c u)^m\wedge \beta ^{n-m}=F(u,.)d\mu , \end{aligned}$$where $$\mu $$ is a positive Borel measure defined on an m-hyperconvex domain of $${\mathbb {C}}^{n}$$, m is an integer such that $$1\le m\le n$$ and $$\beta :=dd^{c}\vert z\vert ^{2}$$ is the standard kähler form in $${\mathbb {C}}^{n}. $$ We show that, under some regularity conditions on the density F, if this equation admits a (weak) subsolution in $$\Omega $$, then it admits a (weak) solution with a prescribed least maximal m-subharmonic majorant in $$\Omega $$. Complex Hessian equations -subharmonic functions Dirichlet problem -hyperconvex domain Maximal -subharmonic function Asserda, Saïd aut El Gasmi, Ayoub (orcid)0000-0003-0453-2074 aut Enthalten in Complex analysis and operator theory Springer International Publishing, 2007 14(2020), 8 vom: 13. Okt. (DE-627)565301047 (DE-600)2425163-X (DE-576)409490164 1661-8254 nnns volume:14 year:2020 number:8 day:13 month:10 https://doi.org/10.1007/s11785-020-01044-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 14 2020 8 13 10 |
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Abstract We study the complex equations of Hessian type (ddcu)m∧βn-m=F(u,.)dμ,$$\begin{aligned} (dd^c u)^m\wedge \beta ^{n-m}=F(u,.)d\mu , \end{aligned}$$where $$\mu $$ is a positive Borel measure defined on an m-hyperconvex domain of $${\mathbb {C}}^{n}$$, m is an integer such that $$1\le m\le n$$ and $$\beta :=dd^{c}\vert z\vert ^{2}$$ is the standard kähler form in $${\mathbb {C}}^{n}. $$ We show that, under some regularity conditions on the density F, if this equation admits a (weak) subsolution in $$\Omega $$, then it admits a (weak) solution with a prescribed least maximal m-subharmonic majorant in $$\Omega $$. © Springer Nature Switzerland AG 2020 |
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Abstract We study the complex equations of Hessian type (ddcu)m∧βn-m=F(u,.)dμ,$$\begin{aligned} (dd^c u)^m\wedge \beta ^{n-m}=F(u,.)d\mu , \end{aligned}$$where $$\mu $$ is a positive Borel measure defined on an m-hyperconvex domain of $${\mathbb {C}}^{n}$$, m is an integer such that $$1\le m\le n$$ and $$\beta :=dd^{c}\vert z\vert ^{2}$$ is the standard kähler form in $${\mathbb {C}}^{n}. $$ We show that, under some regularity conditions on the density F, if this equation admits a (weak) subsolution in $$\Omega $$, then it admits a (weak) solution with a prescribed least maximal m-subharmonic majorant in $$\Omega $$. © Springer Nature Switzerland AG 2020 |
| abstract_unstemmed |
Abstract We study the complex equations of Hessian type (ddcu)m∧βn-m=F(u,.)dμ,$$\begin{aligned} (dd^c u)^m\wedge \beta ^{n-m}=F(u,.)d\mu , \end{aligned}$$where $$\mu $$ is a positive Borel measure defined on an m-hyperconvex domain of $${\mathbb {C}}^{n}$$, m is an integer such that $$1\le m\le n$$ and $$\beta :=dd^{c}\vert z\vert ^{2}$$ is the standard kähler form in $${\mathbb {C}}^{n}. $$ We show that, under some regularity conditions on the density F, if this equation admits a (weak) subsolution in $$\Omega $$, then it admits a (weak) solution with a prescribed least maximal m-subharmonic majorant in $$\Omega $$. © Springer Nature Switzerland AG 2020 |
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10.1007/s11785-020-01044-9 |
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2024-07-04T06:46:25.619Z |
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