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The boundary Harnack principle for the fractional Laplacian

Krzysztof Bogdan (1997)

Studia Mathematica

We study nonnegative functions which are harmonic on a Lipschitz domain with respect to symmetric stable processes. We prove that if two such functions vanish continuously outside the domain near a part of its boundary, then their ratio is bounded near this part of the boundary.

The Functional Equation

Pavlos Sinopoulos (1987)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

The gradient lemma

Urban Cegrell (2007)

Annales Polonici Mathematici

We show that if a decreasing sequence of subharmonic functions converges to a function in W l o c 1 , 2 then the convergence is in W l o c 1 , 2 .

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