Sharp estimates on the Green functions of perturbations of subordinate Brownian motions in bounded \(\kappa\)-fat open sets
The authors prove the following main result: Under suitable boundedness assumptions for the domain \(D\): if \(Y\) is a symmetric Lévy process with a Lévy density \(J^Y(x)= J(x)+ \sigma(x)\), with \(\sigma\) satisfying: \[ |\sigma|\leq c\max\{|x|^{-d+p},1\},\quad x\in R^d, \] then the \(D\)-domain Green function \(G^Y\) of \(Y^D\) is comparable to the \(D\)-domain Green function \(G^X_D\) of \(X^D\), that is: \[ c^{-1} G^Y_D(x,y)\leq G_D(x,y)\leq c,\;G_D(x,y),\quad x,y\in D, \] for a suitable constant \(c\).
scientific article; zbMATH DE number 6136698
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