engleski

Boundary Harnack principle for subordinate Brownian motions

We establish a boundary Harnack principle for a large class of subordinate Brownian motions, including mixtures of symmetric stable processes, in $\kappa$-fat open sets (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary and the minimal Martin boundary of bounded $\kappa$-fat open sets with respect to these processes with their Euclidean boundaries.

Green functions ; Poisson kernels ; subordinator ; subordinate Brownian motion ; Bernstein functions ; complete Bernstein functions ; symmetric stable processes ; mixture of symmetric stable processes ; harmonic functions ; Harnack inequality ; boundary Harnack principle ; Martin boundary

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