Boundary Harnack inequalities for regional fractional Laplacian 1

@inproceedings{Guan2009BoundaryHI,
  title={Boundary Harnack inequalities for regional fractional Laplacian 1},
  author={Q. S. Guan},
  year={2009}
}
We consider boundary Harnack inequalities for regional fractional Laplacian which are generators of censored stable-like processes on G taking κ(x, y)/|x− y|dxdy, x, y ∈ G as the jumping measure. When G is a C open set, 1 < α < β ≤ 2 and κ ∈ C(G×G) bounded between two positive numbers, we prove a boundary Harnack inequality giving dist(x, ∂G) order decay for harmonic functions near the boundary. For a C open set D ⊂ D ⊂ G, 0 < α ≤ (1 ∨ α) < β ≤ 2, we prove a boundary Harnack inequality giving… CONTINUE READING

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