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- W3100195468 abstract "Let $$Omega $$ be an unbounded domain in $$mathbb {R}times mathbb {R}^{d}.$$ A positive harmonic function u on $$Omega $$ that vanishes on the boundary of $$Omega $$ is called a Martin function. In this note, we show that, when $$Omega $$ is convex, the superlevel sets of a Martin function are also convex. As a consequence we obtain that if in addition $$Omega $$ has certain symmetry with respect to the t-axis, and $$partial Omega $$ is sufficiently flat, then the maximum of any Martin function along a slice $$Omega cap ({t}times mathbb {R}^d)$$ is attained at (t, 0)." @default.
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- W3100195468 date "2018-01-12" @default.
- W3100195468 modified "2023-10-04" @default.
- W3100195468 title "Convexity of level lines of Martin functions and applications" @default.
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- W3100195468 doi "https://doi.org/10.1007/s13324-017-0207-3" @default.
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