Convexity estimates for the Green’s function

In this paper, for the Green’s function of a bounded convex domain Ω with pole at x 0 ∈ Ω , we find the auxiliary curvature function which satisfies a differential inequality and so attains its minimum on the boundary. Moreover, we obtain a convexity estimate for the Green’s function of the domain a...

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 53; no. 3-4; pp. 675 - 688
Main Author Shi, Shujun
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2015
Springer Nature B.V
Subjects
Analysis
Calculus of variations
Calculus of Variations and Optimal Control; Optimization
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Partial differential equations
Systems Theory
Theoretical
35E10
35J05
35B30
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Summary:In this paper, for the Green’s function of a bounded convex domain Ω with pole at x 0 ∈ Ω , we find the auxiliary curvature function which satisfies a differential inequality and so attains its minimum on the boundary. Moreover, we obtain a convexity estimate for the Green’s function of the domain above and give the proof of its specific convexity from the viewpoint of partial differential equations themselves.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-014-0763-4