Properties of Solutions to a Harmonic-Mapping Type Equation with a Dirichlet Boundary Condition

Properties of Solutions to a Harmonic-Mapping Type Equation with a Dirichlet Boundary Condition

In the present paper, we consider the problem where β 1 , β 2 > 0 and β 1 + β 2 < 1, and Ω is a convex domain in ℝ n . The existence, uniqueness, regularity and -concavity of the positive solutions of the problem (0.1) are proven.

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Veröffentlicht in:Acta mathematica scientia 2023-05, Vol.43 (3), p.1161-1174
Hauptverfasser: Chen, Bo, Chen, Zhengmao, Xie, Junhui
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Mathematics
Mathematics and Statistics
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Zusammenfassung:In the present paper, we consider the problem where β 1 , β 2 > 0 and β 1 + β 2 < 1, and Ω is a convex domain in ℝ n . The existence, uniqueness, regularity and -concavity of the positive solutions of the problem (0.1) are proven.
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-023-0310-5