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The boundary Harnack principle for the fractional Laplacian

100%

Bogdan K.

Studia Mathematica

1997

tom 123

nr 1

43-80

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.

Scattering properties for a pair of Schrödinger type operators on cylindrical domains

100%

Melgaard M.

Open Mathematics

2007

tom 5

nr 1

134-153

Strong asymptotic completeness is shown for a pair of Schrödinger type operators on a cylindrical Lipschitz domain. A key ingredient is a limiting absorption principle valid in a scale of weighted (local) Sobolev spaces with respect to the uniform topology. The results are based on a refined version of Mourre’s method within the context of pseudo-selfadjoint operators.

Ograniczanie wyników

1 Open Mathematics

1 Studia Mathematica

1 Bogdan K.

1 Melgaard M.

1 2007

1 1997

Wyniki wyszukiwania

The boundary Harnack principle for the fractional Laplacian

Scattering properties for a pair of Schrödinger type operators on cylindrical domains