Projekt per år
Sammanfattning
On bounded B-regular domains, we study envelopes of plurisubharmonic functions bounded from above by a function ϕ which is continuous in the extended reals on the closure of the domain. For ϕ satisfying certain additional criteria limiting its behavior at the singularities, we establish a set where the Perron–Bremermann envelope Pϕ is guaranteed to be continuous. This result is a generalization of a classic result in pluripotential theory due to J. B. Walsh. As an application, we show that the complex Monge–Ampère equation (ddcu)n=μbeing uniquely solvable for continuous boundary data implies that it is also uniquely solvable for a class of boundary values continuous in the extended reals and unbounded from above.
Originalspråk | engelska |
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Sidor (från-till) | 3959-3971 |
Antal sidor | 13 |
Tidskrift | Mathematische Zeitschrift |
Volym | 301 |
Nummer | 4 |
DOI | |
Status | Published - 2022 aug. |
Ämnesklassifikation (UKÄ)
- Matematisk analys
Fingeravtryck
Utforska forskningsämnen för ”Continuity of envelopes of unbounded plurisubharmonic functions”. Tillsammans bildar de ett unikt fingeravtryck.Projekt
- 1 Aktiva
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Randsingulariteter för plurisubharmoniska funktioner
Wikström, F. (Forskare) & Nilsson, M. (Forskare)
2019/01/01 → …
Projekt: Forskning
Aktiviteter
- 1 Handledning av forskarstuderande
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Randsingulariteter av plurisubharmoniska funktioner
Wikström, F. (Första/primär/huvudhandledare) & Christiansen, J. S. (Andra handledare)
2018 sep. 15 → 2023 sep. 15Aktivitet: Examination och handledarskap › Handledning av forskarstuderande