Two-sided heat kernel estimates for censored stable-like processes
Let \(D\subset \mathbb R^d\) be an open subset. A censored \(\alpha\)-stable-like process in \(D\) is a strong Markov process whose infinitesimal generator is given by \[ (L_D^\alpha u)(x)=\lim_{\varepsilon \to 0}\int_{y\in D:\;|y-x|>\varepsilon}(u(y)-u(x))\frac{C(x,y)}{|x-y|^{d+\alpha }}\,dy,\quad u\in C_0^2(D), \] where \(C(x,y)\) is a measurable symmetric function on \(D\times D\), \(0<C_1\leq C(x,y)\leq C_2<\infty\). Under various assumptions, the authors find sharp two-sided estimates for the transition densities and Green functions of such processes.
scientific article; zbMATH DE number 5668288
scientific article