Naslov
Martin Kernel and Infima of Positive Harmonic Functions

Autori
Vondraček, Zoran

Izvornik
Transactions of the American mathematical society (0002-9947) 335 (1993), 2; 547-557

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Positive harmonic functions ; Martin kernel

Sažetak
Let $D$ be a bounded Lipschitz domain in $\bbr^n$ and let $K(x, z), \ x\in D, \ z\in \partial D$, be the Martin kernel based at $x_0\in D$. For $x, y\in D$, let $k(x, y)=\inf\{; ; ; ; ; h(x): h \mbox{; ; ; ; ; positive harmonic in}; ; ; ; ; \ D$, $h(y)=1\}; ; ; ; ; $. We show that the function $k$ completely determines the family of positive harmonic functions on $D$. Precisely: for every $z\in \partial D$, $\lim_{; ; ; ; ; y\rightarrow z}; ; ; ; ; k(x, y)/k(x_0, y)=K(x, z)$. The same result is true for second order uniformly elliptic operators and Schr\"{; ; ; ; ; o}; ; ; ; ; dinger operators.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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